Engineering Drawing previous year questions

(Unit-2- Projections of Points, Lines & Planes)

2019

1. A point P is 10 mm above HP and 25 mm in front of VP. Point Q is 50 mm above HP and 45 mm in front of VP. The distance between the projectors is 55 mm. Draw the projections and draw the projection of line joining P & Q.

 

2. The top view of a 75 mm long line AB measures 65 mm, while its front view measures 50 mm. Its one end A is in HP and 12 mm in front of VP. Draw the projections of AB and determine it’s with HP and VP.

 

3. A hexagonal lamina of 20 mm side rests on one of its corners on the HP. The diagonal passing through this corner is inclined at 45° to HP. The lamina is then rotated through 90° such that the top view of this diagonal is perpendicular to the VP and the surface is still inclined at 45° to the HP. Draw the projections of the lamina.

 

4. A point P is 20 mm below HP and lies in the third quadrant; its shortest distance from xy is 40 mm. Draw its projections.

 

5. A line AB 120 mm long is inclined at 45° to HP and 30° to VP. Its midpoint C is in VP and 20 mm above HP. The end A is in third quadrant and B is in first quadrant. Draw the projections of the line.

 

6. Hexagonal lamina of 25 mm side has its surface inclined at 30° to HP. Its one side is parallel to HP and inclined at 45° to VP. Draw its projections.

 

7. (a) Two points A and B are in the HP. The point A is 30 mm in front of the VP. While B is behind the VP. The distance between their projectors is 75 mm and the line joining their top views makes an angle of 45° with xy. Find the distance of the point B from the VP.

 

(b) A line AB 55 mm long makes an angle of 30° to HP and 45° to VP. The end A is 12 mm in front of VP and 15 mm above HP. Draw the projection of the line.

 

8. A hexagonal lamina of 20 mm side rests on one of its corners on the HP. The diagonal passing through this corner is inclined at 45° to HP. The lamina is then rotated through 90° such that the top view of this diagonal is perpendicular to the VP and the surface is still inclined at 45° to the HP. Draw the projections of the lamina.

 

9. A thin rectangular plate of sides 50 mm x 25 mm has its shorter side in the HP and inclined at an angle of 30° to the VP. Project its front view when its top view is a perfect square of 25 mm side.

2018 

10. Draw the projections of the following point on a common reference line:

(i) Point A is 40 mm above HP and 60 mm in front of VP

(ii) Point A lying on HP and 25 mm in front of VP.

(iii) Point A lying on VP and 70 mm above HP.

(iv) Point C is 40 mm below HP and 30 mm behind VP.

(v) Point A is in V.P and 55 mm above H.P

 

11. Draw the projections of straight line AB 60 mm long parallel to HP and inclined at an angle of 40° to VP. The end A is 30 mm above HP and 20 mm in front of VP.

 

12. A pentagonal plane ABCDE 35 mm side has its plane inclined 50° to H.P. Its diameter joining the vertex B to the midpoint F of the base DE is inclined at 25° to the xy-line. Draw its projections keeping the corner B nearer to VP.

 

13. Draw the projections of the following point on a common reference line:

(i) Point P is 20 mm above H.P and 30 mm infront of VP

(ii) Point Q is 35 mm above H.P and 45 mm behind VP

(iii) Point R is 42 mm below H.P and 55 mm behind VP

(iv) Point S is 35 mm below H.P and 52 mm infront of VP

(v) Point V is in V.P and 45 mm above HP.

 

14. A line AB of 70 mm long has its end A at 10 mm above H.P and 15 mm in front of V.P. Its front view and top view measure 50 mm and 60 mm respectively. Draw the projections of the line and determine its inclinations with H.P and V.P.

 

15. A pentagonal plane ABCDE 45 mm side has its plane inclined 45° to H.P. Its diameter joining the vertex B to the midpoint F of the base DE is inclined at 30° to the xy-line. Draw its projections keeping the corner B nearer to VP.

 

16. Draw the projections of a point Q, which is 45 mm above HP and 15 mm behind VP

 

17.Draw the projections of a point R, which is 40 mm below HP and 15 mm behind VP.

 

18. Draw the projections of a line CD 60 mm long parallel to HP and inclined at 35 to VP. C is 20 mm above HP and 15 mm in front of VP.

 

19. Point A of the line AB is 5 mm above HP and 15 mm in front of VP. Point B is 30 mm above HP and 45 mm in front of VP. The front and top views lie in the same projector. Draw the projections and find the true length and true inclinations.

 

20. A point P is 20 mm above HP and 15 mm in front of VP. Draw the front view, top view and left side view.

 

21.A point P is 10 mm above HP and 25 mm in front of VP. Point Q is 50 mm above HP and 45 mm in front of VP. The distance between the projectors is 55 mm. Draw the projections and draw the projection of line joining P & Q.

 

22. A 60 mm long line AB is parallel to VP and inclined at 30° to HP. One end A is 30 mm above HP and 15 mm in front of VP. Draw the projections of the line.

 

23.End A of a line AB is 10 mm above HP and 20 mm in front of VP. The other end B is 45 mm above HP and 65 mm in front of VP. The distance between the projections and find the length and true inclinations.

 

 

 

 

INTERPENETRATION OF SOLIDS

INTERPENETRATION OF SOLIDS

1. A square prism of base 50 mm side and height 125 mm stands on the ground with its side of base inclined at an angle of 30⁰ to VP. It is penetrated by a cylinder of diameter 50 mm and axis 125 mm long. The axis of the cylinder is parallel to both HP and VP and bisects the axis of the prism. Draw the projection showing fully the curves of intersection.

2. Two cylinders each of 30 mm diameter and altitude 80 mm intersect each other at right angles. Their axes bisect each other and are parallel to VP. Determine the line of intersection of the two cylinders. Also, develop the lower portion of the vertical cylinder, neglecting the thickness of the metal.

3. (a) A vertical cylinder of diameter 80 mm intersects a horizontal cylinder of diameter 40 mm. The shortest distance between their axes is 40 mm. Draw the projections showing the intersection profile.

(b) A horizontal cylinder of 50 mm diameter penetrates a vertical cylinder of 75 mm diameter resting on HP. The two axes are coplanar. The axis of the horizontal cylinder is 50 mm above the HP. draw the projections showing the curves of intersection.

4. A cylindrical boiler is 2m in diameter and has a cylindrical dome 0.8m diameter and 0.6m high. The axis of the dome intersects the axis of the boiler. Draw three views of the arrangement. Also develop the surface of the dome. Take a scale of 1 cm = 0.2 m.

5. A cylinder of 60 mm diameter and 100 mm height stands on its base on the ground. It is penetrated centrally by a cylinder of 40 mm diameter and 100 mm long, whose axis is parallel to HP, but inclined at an angle of 30⁰ to VP. Draw the projections showing the curves of intersection. Also draw the development of the penetrating cylinders.

6. A hexagonal prism of side of base 30 mm is resting on one of its bases on HP with a face parallel to VP. The prism contains a square hole of 20 mm side. The axis of the hole is parallel to VP and inclined at an angle of 30⁰ to the HP intersecting the axis of the prism. The faces of the hole are equally inclined to VP. Draw the lines of intersection.

7. A square prism of base 50 mm side and height 125 mm stands on the ground with its side of base inclined at an angle of 30⁰ to VP. It is penetrated by a cylinder of diameter 50 mm and axis 125 mm long. The axis of the cylinder is parallel to both HP and VP and bisects the axis of the prism. Draw the projection showing fully the curves of intersection.

8. A cylinder of 60 mm diameter stands vertically on its base. It is pierced by a horizontal square prism of 35 mm side of base such that the axes of the two solids intersect each other at right angles. A face of the prism is inclined at an angle of 60⁰ to HP and 300 to VP. Draw the projections of the solids, showing the lines of intersection.

9. A cylinder of 60 mm diameter and axis 80 mm long is standing on its base on HP. A horizontal rectangular hole of 35 mm x 25 mm sides is cut through the cylinder. Axis of the hole is parallel to VP. The axes of both cylinder and hole intersect at right angles and bisect each other. Draw the projections and show the curves of intersection.

10. A cylinder of 60 mm diameter and axis 80 mm long is standing on its base on HP. A horizontal hexagonal hole of 25 mm side is cut through the cylinder. Axis of the hole is parallel to VP. The axes of both cylinder and hole intersect at right angles and bisect each other. A side face of the hole is inclined at an angle of 30⁰ to the HP. Draw the projections and show the curves of intersection.

11. A square hole of 35 mm side is cut in a cylindrical shaft of 60 mm diameter and 100 mm long. The axis of the hole intersects that of the shaft at right angles. All the faces of the hole are inclined at 45⁰ to HP. Draw the projections of the shaft when an imaginary plane containing the two axes is parallel to VP.

12. A vertical square prism of side of base 60 mm is penetrated by a horizontal triangular prism of 40 mm side. The axes are 5 mm apart. One rectangular face of the vertical prism is inclined at an angle of 60⁰ to VP, while that of the horizontal prism is parallel to VP. Draw the projections showing the lines of intersection.

13. A vertical hexagonal prism, side of base 30 mm and 60 mm long, is completely penetrated by a horizontal square prism of 27 mm side and 90 mm length. The axis of the horizontal prism is parallel to VP and 5 mm in front of the axis of the hexagonal prism. If one rectangular face of the hexagonal prism is parallel to VP and all the faces of the square prism are equally inclined to HP, draw the projections of the prisms showing the lines of intersection.

14. (a) A right circular cylinder of 60 mm diameter penetrates another cylinder of 80 mm diameter. Their axes are at right angles to each other, but 8 mm apart. Draw the projections of the curves of intersection on a plane parallel to the axes of the cylinders.

(b) A vertical pipe, 60 mm diameter has a horizontal branch of 40 mm diameter on one side. The axis of the horizontal pipe is 6 mm from the axis of the main pipe and parallel to VP. Draw the projections of the pipe showing the curves of intersection.

15. A vertical pipe of 64 mm diameter is welded to another pipe of diameter 32 mm. The axis of the second pipe is inclined at 60⁰ to HP, parallel to VP. Draw the projections showing the curves of intersection.

16. A vertical square prism, base 50 mm side, has a face inclined at 30⁰ to the VP. It has a hole of 65 mm diameter drilled through it. The center line of the hole is parallel to both the HP and the VP and is 5 mm away from the axis of the prism. Draw the projections of the prism and show the curves of intersection.

17. A vertical cylinder of 60 mm diameter is penetrated by a square prism of 35 mm side. The axis of the prism is inclined at an angle of 30⁰ to the ground, but parallel to the VP. The faces of the prism are equally inclined to the VP and the axis of the prism is 10mm in front of the axis of the cylinder. Draw the projections of the solids showing the curves of interpenetration.

18. A right circular cone of base 50 mm and altitude 80 mm standing on HP with its axis vertical is penetrated by a cylinder of diameter 20 mm such that the axes intersect at an angle of 60⁰ at a height of 35 mm from the base and the plane containing the axes is parallel to VP. Draw the curves of intersection.

19. A hexagonal prism, having base with a 40 mm side and a 100 mm long axis, is resting on its base on the H.P. with a side of the base parallel to the V.P. It is penetrated by a square prism having base with a 35 mm side and a 100 mm long axis such that the axes of both the prism intersect each other at right angles. The faces of the square prism is equally inclined to the H.P. Draw the projections of the combination and show the lines of intersection.

20. A pentagonal prism, having base with a 45 mm side and a 100 mm long axis, is resting on its base on the H.P. with a side of the base parallel to the V.P. It is penetrated by a square prism having base with a 35 mm side and a 100 mm long axis, such that the axes of both the prism bisect each other at right angles. The faces of the square prim are equally inclined to the H.P. Draw the projections of the combination and show the lines of intersection.

21. A square prism, having base with a 50 mm side, is resting on its base on H.P. with the faces equally inclined to the V.P. It is completely penetrated by a horizontal cylinder with a 50 mm base diameter such that their axes of bisect each other at right angles. Assuming suitable lengths of both the solids, draw their projections and show the curves of intersection.

22. A square prism, having base with a 60 mm side and a 100 mm long axis, is resting on its base on H.P. with the faces equally inclined to the V.P. It is completely penetrated by a hexagonal prism having base with a 30 mm side and a 100 mm long axis having a face parallel to H.P. The axes of the prisms bisect each other at right angles. Draw their projections and show the curves of intersection.

23. A cylinder of 60mm diameter, having its axis vertical is penetrated by another cylinder of 40mm diameter. The axis of the penetrating cylinder is parallel to V.P and bisects the axis of the vertical cylinder making an angle of 60⁰ with it. Draw the projections showing the curves of intersection.

24. A cylindrical boiler is 2m in diameter and has a cylindrical dome 0.8m diameter and 0.6m high. The axis of the dome intersects the axis of the boiler. Draw three views of the arrangement. Also develop the surface of the dome. Take a scale of 1 cm = 0.2 m.

25. A cylinder of 60 mm diameter and 100 mm height, stands on its base on the ground. It is penetrated centrally by a cylinder of 40 mm diameter and 100 mm long, whose axis is parallel to HP, but inclined at an angle of 300 to VP. Draw the projections showing the curves of intersection. Also draw the development of the penetrating cylinders.

26. A square prism of base 50 mm side and height 125 mm stands on the ground with its side of base inclined at an angle of 300 to VP. It is penetrated by a cylinder of diameter 50 mm and axis 125 mm long. The axis of the cylinder is parallel to both HP and VP and bisects the axis of the prism. Draw the projection showing fully the curves of intersection.

27. A cylinder of 60 mm diameter stands vertically on its base. It is pierced by a horizontal square prism of 35 mm side of base such that the axes of the two solids intersect each other at right angles. A face of the prism is inclined at an angle of 600 to HP and 300 to VP. Draw the projections of the solids, showing the lines of intersection.

28. A vertical square prism, base 50 mm side has its faces equally inclined to the V.P. It is completely penetrated by another square prism of base 30 mm side, the axis of which is parallel to both the planes and is 6 mm away from the axis of the vertical prism. The faces of the horizontal prism also are equally inclined to the V.P. Draw the projections of the solids showing lines of intersection.

29. Two equal prisms whose ends are equilateral triangles of 40 mm side and axes 100 mm long, intersect at right angles. One face of each prism is on the ground. The axis of one of the prisms makes 300 with the V.P. Draw three views of the solids.

30. A square prism of base 50 mm side and height 125 mm stands on the ground with a side of the base inclined at 300 to the V.P. It is penetrated by a cylinder, 50mm diameter and 125 mm long, whose axis is parallel to both the H.P. and the V.P. and bisects the axis of the prism. Draw the projections showing fully the curves of intersection.

31. A cylinder of 75 mm diameter and 125 mm height, stands on its base on the ground. It is penetrated centrally by a cylinder, 50 mm diameter and 125 mm long, whose axis is parallel to the H.P. but inclined at 300 to the V.P. Draw the projections showing curves of intersection. Draw also the development of the surface penetrated cylinder.

32. A right circular cylinder of 75 mm diameter penetrates another of 100 mm diameter, their axes being at right angles to each other but 10 mm apart. Draw the projections of the curves of intersection on a plane parallel to the axes of the cylinders.

33. Two circular pipes of 75 mm and 50 mm diameters (inside) meet at 300. The axes of both the pipes are in one plane and the 75mm pipe is vertical. The thickness of the pipes is 6 mm in both cases. Draw the projections showing curves of intersection.

34. A square hole of 35 mm side is cut in a cylindrical shaft 75 mm diameter and 125 mm long. The axis of the hole intersects that of the shaft at right angles. All faces of the hole are inclined at 450 to the H.P. Draw three views of the shaft when the plane of the two axes is parallel to the V.P.

35. Two equal triangular prisms whose axes intersect each other at right angles, have side of base 40 mm and altitude 100 mm. The vertical prism has one edge of its base perpendicular to VP. The horizontal prism has one of its rectangular faces vertical, making an angle of 300 with V.P.

Draw the projections showing the lines of intersection.

36. A hexagonal prism of side of base 30 mm is resting on one of its bases on HP with a face parallel to VP. The prism contains a square hole of 20 mm side. The axis of the hole is parallel to VP and inclined at an angle of 300 to the HP intersecting the axis of the prism. The faces of the hole are equally inclined to VP. Draw the lines of intersection

37. A square pipe of 60 mm side is connected to another square pipe of side 45 mm. The axis of bigger pipe is vertical and the axis of the smaller pipe intersects the axis of the bigger pipe at an angle of 450. All the faces of both the pipes are equally inclined to VP. Draw the projections showing the lines of intersection.

38. Two cylinders each of 30 mm diameter and altitude 80 mm intersect each other at right angles. Their axes bisect each other and are parallel to VP. Determine the line of intersection of the two cylinders. Also, develop the lower portion of the vertical cylinder, neglecting the thickness of the metal.

39. (a) A vertical cylinder of diameter 80 mm intersects a horizontal cylinder of diameter 40 mm. The shortest distance between their axes is 40 mm. Draw the projections showing the intersection profile.

(b) A horizontal cylinder of 50 mm diameter penetrates a vertical cylinder of 75 mm diameter resting on HP. The two axes are coplanar. The axis of the horizontal cylinder is 50 mm above the HP. Draw the projections showing the curves of intersection.

40. A cylinder of 60 mm diameter and axis 80 mm long is standing on its base on HP. A horizontal rectangular hole of 35 mm x 25 mm sides is cut through the cylinder. Axis of the hole is parallel to VP. The axes of both cylinder and hole intersect at right angles and bisect each other. Draw the projections and show the curves of intersection.

41. A cylinder of 60 mm diameter and axis 80 mm long is standing on its base on HP. A horizontal hexagonal hole of 25 mm side is cut through the cylinder. Axis of the hole is parallel to VP. The axes of both cylinder and hole intersect at right angles and bisect each other. A side face of the hole is inclined at an angle of 300 to the HP. Draw the projections and show the curves of intersection.

42. A cylindrical pipe of 36 mm diameter has a similar branch of the same size. The axis of the branch intersects the axis of the main pipe at an angle of 600. Draw the projections, when the two axes lie in a plane parallel to the VP and the axis of the main pipe is vertical. Also, develop the surfaces of the two pipes assuming suitable lengths.

43. A square hole of 35 mm side is cut in a cylindrical shaft of 60 mm diameter and 100 mm long. The axis of the hole intersects that of the shaft at right angles. All the faces of the hole are inclined at 450 to HP. Draw the projections of the shaft when an imaginary plane containing the two axes is parallel to VP.

Orthographic Projections - Diagrams

Isometric Projections

ISOMETRIC PROJECTIONS

1. A hexagonal prism , side of base 25 mm and height 50 mm rests on H.P. and one of the edges of its base is parallel to V.P .A section plane perpendicular to V.P. and inclined at 50⁰ to H.P bisects the axis of the prism . Draw the isometric projection of the truncated prism. Draw the isometric projection of the truncated prism.

2. A cone radius of base 25 mm and axis 50 mm long rests with one of its base edges on H.P. Its axis is parallel to V.P. Draw the isometric projection of the solid (i) showing the tip towards viewer (ii) when it rests with its base on H.P.

 3. Draw the isometric projection of a hexagonal prism of side of base 35mm and altitude 50mm surmounting a tetrahedron of side 45mm such that the axes of the solids are collinear and at least one of the edges of the two solids are parallel.

4. A square pyramid of side 30mm, axis length 50mm is centrally placed on top of a cube of side 50mm. Draw the isometric projections of solids.

5. A triangular prism of base edge 30mm and height 60mm stands on one of its corners on the ground with the axis inclined at 300 to the HP and 450 to the VP. The base of the object is nearer to VP compared to the top. Draw an isometric view of the object.

6. The frustum of a hexagonal pyramid side of top and bottom 25 mm and 40 mm respectively with axis 50 mm height rests on its base in H.P. Its axis is parallel to V.P. A sphere of diameter 40 mm is placed centrally on top of the prism. Draw the isometric projection of the solid.

7. A hexagonal prism, side of base 25 mm and axis 50 mm long rests on its base in H.P. Its axis is parallel to V.P. Draw the isometric projection of the solid. Show the isometric scale.

8. Draw the isometric view of a Door-Steps having three steps of 22cm tread and 15cm rise. The steps measure 75cm width-wise.

9. Draw the isometric view of a square prism, with side of base 40mm and length of axis 70mm, when its axis is (i) vertical and (ii) horizontal.

10. Draw the isometric view of a hexagonal prism, with side of base 25mm and axis 60mm long, the prism is resting on its base on H.P. with an edge of the base parallel to V.P. (Use the box method).

11. Draw the isometric view of a cylinder of base 50 mm diameter and 70mm height when it rests with its base on H.P. (use four-center method). Show the isometric scale.

12. Draw the isometric view of a pentagonal pyramid, with side of base 25mm and axis 60mm long. The pyramid is resting on its base on H.P, with an edge of the base (away from the observer) parallel to V.P. (Use off-set method).

UNIT_II - Projection of Points & Lines

UNIT_II

PROJECTION OF POINTS:

1. Draw the projections of the following points on the same line, keeping the Projectors 20mm apart.

(a) Point C, in V.P. and 40mm above H.P. 

(b) Point D, 25mm below the H.P. and 25mm behind the V.P.

(c) Point E, 15mm above H.P. and 50mm behind V.P.

(d) Point F, 40mm below H.P. and 25mm in front of V.P.

2.   (a) A point A is 2.5 cm above the H.P. and 3 cm in front of the V.P. Draw its Projections.

(b) A point A is 2 cm below the H.P. and 4 cm behind the V.P. Draw its Projections.

3.   (a) A point P is 15mm above the H.P. and 20mm in front of the V.P. Another point Q is 25mm behind the V.P. and 40mm below the H.P. Draw projections of P and Q keeping the distance between their projectors equal to 90mm.Draw straight lines joining i. their top views and ii. their front views.

(b) A point 30mm above XY line is the plan view of two points P and Q. the elevation of P is 45mm above the H.P. while that of the point Q is 35mm below the H.P. Draw the projections of the points and state their position with reference to the principal planes and the quadrant in which they lie.

4.   Two points P and Q are in the H.P. The point P is 30 mm in front of V.P. and Q is behind the V.P. The distance between their projectors is 80 mm and line joining their top views makes an angle of 40⁰ with XY. Find the distance of the point Q from the V.P.

5.   (a) A point A is 20mm above H.P. and in I quadrant. Its shortest distance from the reference line XY is 40mm. Draw the projections of the point and determine its distance from V.P.

(b) A point at 25mm above the reference line XY is the front view of two points A and B. The top view of A is 40mm behind V.P and the top view of B is 50mm in front of V.P. Draw the projections of the points and state their positions relative to the planes of projection and the quadrants in which they lie.

6.   A point P is 20mm below HP and lies in III quadrant. Its shortest distance from xy is 40mm. Draw its projections.

7.  (a) Draw the projections of the following points on the same ground line, keeping the Projectors 25mm apart.     (i). A, in the H.P. and 20 mm behind the V.P.

(ii). B, 40mm above the H.P. and 25mm in front of the V.P.

(b) State the quadrants with the help of drawing, in which the following points are situated

                         i.      A point P; its top view is 40mm above xy; the front view 20 mm below the top view.

                        ii.      A point Q; its projections coincide with each other 40mm below xy.

8.  (a) The point A is on H.P. and 40mm in front of V.P. Another point B is on V.P. and below H.P. The line joining their front views makes an angle of 45⁰ with x y, while the line joining their top views makes an angle of 30⁰. Find the distance of the point B from H.P.

(b) Draw the projections of the following points in III quadrant when the

                 i. Point A lies in the H.P. and 22mm away from V.P. 

                ii. Point B lies in V.P. and 32mm away from H.P.

               iii   Point C lies 32mm from H.P. and 22mm from V.P.

9.  (a) A point P is 15mm above the H.P. and 20mm in front of the V.P. Another point Q is 25mm behind the V.P. and 40mm below the H.P. Draw projections of P and Q keeping the distance between their projectors equal to 90mm. Draw straight lines joining i. their top views and ii. their front views.

(b) A point 30mm above xy line is the plan view of two points P and Q. the elevation of P is 45mm above the H.P. while that of the point Q is 35mm below the H.P. Draw the projections of the points and state their position with reference to the principal planes and the quadrant in which they lie.

10. (a) Two points A and B are on H.P; the point  A being 30mm in front of V.P., while B is 45mm behind V.P. The line joining their top views makes an angle of 45⁰ with xy. Find the horizontal distance between two points.

(b) Find the distance between two points A and B when B is 40mm in front of V.P. and 25mm above H.P. The point A is 25mm behind the V.P. and 40mm below H.P. The distance between projectors measured along xy line being 40mm.

11.(a) Draw the projectors of the following points in different quadrants.

                  i.      Point A, 25mm in front of V.P., 30mm above H.P

                 ii.      Point B, 22mm behind V.P., 28mm above H.P.

                iii.      Point C, 28mm behind V.P., 30mm below H.P 

                 iv.      Point D, 40mm in front of V.P., 25mm below H.P

(b) A point P is 25mm in front of the V.P. and 40 mm above the H.P. Another point Q is 40mm in front of the V.P. and 25mm above the H.P. The distance measured between the projectors is 40mm. Draw the projections and find the distance between P and Q.

PROJECTION OF LINES:

1. (a) A line CD measures 80mm is inclined at an angle of 30⁰ to HP and 45⁰ to VP. The point C is 20mm above HP and 30mm in front of VP. Draw the projections of the line.

(b) Draw the projections of a line JK 70 mm long and touching both HP and VP. It is inclined at 40⁰ to HP and 35⁰ to VP.

2.  A line AB is 30 mm long and inclined at 30⁰ to VP and parallel to HP. The end A of the line is 15 mm above HP and 20mm in front of VP. Draw the projections.

3.  (a) A line CD is parallel to VP and inclined at 40⁰ to HP. C is in HP and 25 mm in front of VP. The length of the top view is 50mm. Determine its true length.

(b) A line measuring 80 mm long has one of its ends 60mm above HP and 20mm in front of VP. The other end is 15 mm above HP and in front of VP. The front view of the line is 60 mm long. Draw the top view.

4.  (a) A line AB 25mm long is perpendicular to V.P. and parallel to H.P. Its end A is 10mm in front of V.P. and the line is 20mm above H.P. Draw the projections of the line.

(b) A line MN 50mm long is parallel to V.P. and inclined at 30⁰ to H.P. The end M is 20mm above H.P. and 10mm in front of V.P. Draw the projections of the line.

5.  (a) A line AB, 65 mm long has its end A in the H.P. and 15 mm in front of the V.P. The end B is in III quadrant. The line is inclined at 30⁰ to the H.P. and at 60⁰ to the V.P. Draw its projections.

(b) A line PQ 75 mm long has its end P in both HP and VP. It is inclined at an angle of 30⁰ to HP and 45⁰ to VP. Draw projections of the line.

6. The distance between the projectors of two points A and B is 70 mm. Point A is 10 mm above HP and 15 mm in front of VP. Point B is 50 mm above HP and 40 mm in front of VP. Find the shortest distance between A and B. Measure true inclination of the line AB with HP and VP.

7. (a) The line EF 60 mm long is in VP and inclined to HP. The top view measures 45 mm. The end E is 15 mm above HP. Draw the projections of the line. Find it inclination with HP.

(b) A line AB 60mm long is parallel to HP. The point P is 20mm above HP and 35 mm in front of VP. The length of the front view is 50mm. Determine its true inclination with VP.

8. (a) The length of the top view of a line MN parallel to VP and inclined at 45⁰ to the HP is 50 mm. Point M is 12 mm above HP and 25 mm in front of VP. Draw the projection of the line. Find the true length.

(b) A line GH 45 mm long is in HP and inclined to VP. The end G is 15 mm in front of VP. The length of front view is 35 mm. Draw the projections of the line. Find its inclination with VP.

9.  A 90 mm long line is parallel to and 25 mm in front of V.P. Its one end is in the H.P. while other end is 50 mm above the H.P. Draw the projections of the line and find its inclination with H.P.

10. The length of the top view of a line is 40mm and the length of the front view is 50mm, the top view is inclined at 30⁰ to xy. Draw the projections of the line, assuming that its one end is situated on H.P. and 25mm in front of V.P. Determine the inclinations of the line with H.P and V.P.

11. (a) Draw the projection of a line CD 50 mm long, parallel to HP and inclined to VP. The end of C is 10 mm in front of VP and D is 30 mm in front of VP. The line is 15 mm above HP.

(b) A line AB is 75 mm long. A is 50 mm in front of VP and 15 mm above HP. B is 15mm in front of VP and is above HP. Top view of AB is 50mm long. Draw and measure the front view. Find the true inclinations.

12. (a) A line PQ, 9cm long, is in the H.P. and makes an angle of 30⁰ with the V.P. Its end P is 2.5cm in front of the V.P. Draw its projections.

(b) The front view of a 7.5cm long line measures 5.5cm. The line is parallel to the H.P. and one of its end is in the V.P. and 2.5cm above the H.P. Draw the projections of the line and determine its inclination with V.P. 

13. Two pegs fixed on a wall are 4.5metres apart. The distance between the pegs measured parallel to the floor is 3.6 meters. If one peg is 1.5 meters above the floor, find the height of the second peg and the inclination of the line joining the two pegs, with the floor.

14. A 100 mm long line is parallel to and 40 mm above the H.P. Its two ends are 25 mm and 50 mm in front of the V.P. respectively. Draw the projections of the line and determine its inclination with the V.P.

15. A line AB, 50mm long, has its end A in both the H.P. and the V.P. Its is inclined at 30⁰ to the H.P and at 45⁰ to the V.P. Draw its projections.

16. (a) The top view of a 75 mm long line measures 55 mm. The line is in the V.P., its one end being 25 mm above H.P. Draw its projections.

 (b) The front view of a line, inclined at 3⁰⁰ to the V.P. is 65 mm long. Draw the projection of the line, when it is parallel to and 40 mm above the V.P., its one end being 30mm in front of the V.P.

17. Draw the projections of a 75 mm long straight line, in the following positions:

a.        Parallel to both the H.P. and the V.P. and 25 mm from each.

b.       parallel to 30 mm above H.P. and in the V.P.

c.        parallel to 40 mm in front of V.P. and in the H.P

18. (a) The line EF 60 mm long is in VP and inclined to HP. The top view measures 45 mm. The end E is 15 mm above HP. Draw the projections of the line. Find its inclination with HP.

(b) A line GH 45 mm long is in HP and inclined to VP. The end G is 15 mm in front of VP. The length of the front view is 35 mm. Draw the projections of the line. Determine its inclination with VP.

19. A room measures 8m long, 5m wide and 4m high. An electric bulb hangs in the centre of the ceiling and 1m below it. A thin straight wire connects the bulb to a switch kept in one of corner of the room and 1.25m above the floor. Draw the projections of the wire, also determine its true length and slope with the floor.

20. A line AB, 90 mm long, is inclined at 45⁰ to the HP and its top view makes an angle of 60⁰ with the VP. The end A is in the HP and 12 mm in front of the VP. Draw its front view and find its true inclination with the VP.

21. (a) A line AB is 75 mm long. A is 50 mm in front of VP and 15 mm above HP. B is 15 mm in front of VP and is above HP. Top View of AB is 50mm long. Draw and measure the front view. Find the true inclinations.

(b) A line measuring 80 mm long has one of its ends 60 mm above HP and 20 mm in front of VP. The other end is 15 mm above HP and in front of VP. The front view of the line is 60 mm long. Draw the top view.

22. (a) A line AB 40 mm long is parallel to VP and inclined at 35⁰ to HP. The end A is 15 mm above HP and 20 mm in front of VP. Draw the projections of the line and find its traces.

(b) A line MN 50 mm long is parallel to VP and inclined at 45⁰ to HP. The end M is 20 mm above HP and 15 mm in front of VP. Draw the projections of the line and finds its traces.

23. (a) The line EF 60 mm long is in VP and inclined to HP. The top view measures 45 mm. The end E is 15 mm above HP, Draw the projections of the line. Find its inclination with HP.

(b) A line GH 45 mm long is in HP and inclined to VP. The end G is 15 mm in front of VP. The length of the front view is 35 mm. Draw the projections of the line. Determine its inclination with VP.

24. A line AB of 70mm long, has its end A at 10mm above H.P. and 15mm in front of V.P. Its front view and top view measure 50mm and 60mm respectively. Draw the projections of the line and determine its inclinations with H.P. and V.P.

25. A line AB, 80 mm long, makes an angle of 30⁰ with the V.P. and lies in a plane perpendicular to both the H.P. and the V.P. Its end A is in the H.P. and the end B is in the V.P. Draw its projections.

26. A 95 mm long line is parallel to and 50 mm above the H.P. Its two ends are 20 mm and 50 mm in front of the V.P. respectively. Draw its projections and find its inclination with the V.P.

27. A line PQ, 100mm long, is inclined at 45⁰ to the H.P. and at 30⁰ to the V.P. Its end P is in II quadrant and Q is in IV quadrant. A point R on PQ, 40mm from P is in both the planes. Draw the projections of PQ.

28. A line of 75mm long has one of its ends 50mm in front of V.P. and 15mm above H.P. The top view of the line is 50mm long. Draw and measure the front view. The other end is 15mm in front of V.P. and is above H.P.

29. A line CD 80mm long is inclined at an angle of 30⁰ to H.P. and 45⁰ to V.P. The point C is 20mm above H.P. and 30mm in front of V.P. Draw the projections of the straight line.

30. (a) A line CD 30 mm long is perpendicular to V.P. and parallel to H.P. Its end C is 5mm in front of V.P. and the line is 10mm above H.P. Draw the projections of the line.

(b) A line PQ 40mm long is parallel to V.P. and inclined at an angle of 30⁰ to H.P. The end P is 15mm above H.P. and 20mm in front of V.P. Draw the projections of the line.

31. The projectors of the ends of a line AB are 5cm apart. The end A is 2cm above the H.P. and 3cm in front of the V.P. The end B is 1cm below the H.P. and 4cm behind the V.P. Draw the projections of AB and determine its inclinations with the H.P. and the V.P.

32. (a) A line PQ 75mm long has its end P in the V.P and the end Q in the H.P. The line is inclined at 30⁰ to the H.P. and at 60⁰ to the V.P. Draw its projections.

(b) Draw the projections of a 65mm long straight line, in the following positions:

a.        Parallel to both the H.P and the V.P and 25mm from each.

b.       Perpendicular to the H.P in the V.P and its one end in the H.P.

33. The top view of a line AB, 75mm long measures 50mm. The end A is 40mm in front of VP and 15mm below H.P. B is 15mm in front of V.P. and is above H.P. Draw the projections of the line and determine the distance of B from H.P. and also the inclinations of the line AB with both the planes.

34. A line AB, 65mm long, has its end A 20mm above the H.P. and 25mm in front of the V.P. The end B is 40mm above the H.P. and 65mm in front of the V.P. Draw the projections of AB and show its inclinations with the H.P. and the V.P. 

35. The top view of a 75mm long line AB measures 65mm, while the length of its front view is 50mm. Its one end A is in the H.P. and 12mm in front of the V.P. Draw the projections of AB and determine its inclinations with the H.P. and the V.P.

36. (a) The top view of a 75mm long line measures 55mm. The line is in the V.P., its one end being 25mm above the H.P. Draw its projections.

(b) Draw the projections of a 75mm long line, in the following positions:

a.        Parallel to and 30mm above the H.P and in the V.P.

b.       Inclined at 30⁰ to the H.P and its one end 20mm above the H.P, parallel to and 25mm in front of the V.P.

37. A line AB, 65mm long, has its end A 20mm above the H.P. and 25mm in front of the V.P. The end B is 40mm above the H.P. and 65mm in front of the V.P. Draw the projections of AB and show its inclinations with the H.P. and the V.P.

Mid Point Problems:

38.A line AB 120 mm long is inclined at 45⁰ to HP and 30⁰ to the VP. Its midpoint C is in VP and 20 mm above HP. The end A is in III quadrant and B is in I quadrant. Draw the projections of the line.

39.Draw the projections of a line AB, 90mm long, its midpoint M being 50mm above the H.P. and 40mm in front of V.P. The end A is 20mm above H.P. and 10mm in front of V.P. Show the inclinations of the line with H.P. and V.P.

40. The midpoint of a straight line AB is 60mm above H.P. and 50mm in front of V.P. The line measures 80mm long and inclined at 30⁰ to H.P. and 45⁰ to V.P. Draw its projections.

41. A line of 100mm long makes an angle of 35⁰ with H.P. and 45⁰ with V.P. Its midpoint is 20mm above H.P. and 15mm in front of V.P. Draw the projections of the line.

42. The front view of a 125 mm long line PQ measures 80 mm and its top view measures 100 mm. Its end Q and the midpoint M are in I quadrant, M being 20 mm from both the planes. Draw the projections of the line PQ.