Projection of Lines

Projection of Lines

1.Draw the projections of line 70 mm long when it is parallel to both HP and VP. The line is 20 mm fromboth HP and VP, and one of its ends is 15 mm from PP.

2.Draw the projections of a line 70 mm longwhen it is perpendicular to HP and parallel to VP and 15 mm infront of VP. The end nearer to HP is 20 mm above it and 30 mm infront PP.

3.A line 70 mm long is perpendicular to VP and parallel to HP and 20 mm above it. The end nearer to the observer is 90 mm infront of VP. The line is 15 mm from the PP. Draw its projections.

4.A line, 60 mm long is parallel to VP and inclined at 30° to HP. The end nearer to HP is 10 mm above HP, 15 mm infront of VP and 20 mm from the left PP. Draw the projections of the line on HP, VP and left PP.

5.Draw the projections of a line 65 mm long lying in VP and inclined to HP at 35°. The end which is nearer to HP is 10 mm above it and 80 mm from the right PP.

6.A line 75 mm long is parallel to HP and 16 mm above it and inclined at 40° to VP. The midpoint of the line 50 mm infront VPand 60 mm infront of the right PP. Draw its projections on the three reference planes of projections.

7.Draw the projections of a line 80 mm long when it is in HP and inclined at 50° to VP. One end of the line is 10 mm infront of VPand 20 mm infront the left PP.

8.A line PQ is inclined to HP at 30° and 45° to VP and measures 70 mm. Point P is 20 mmabove HP and 15 mm infront of VP. Draw its projections.

9.Draw the projections of a line AS, 100 mm long inclined at 30° to HP and 45° to VP .Theend A of the line is 20 mm above HP and 25 mm infront of VP. The line slopes upward forward right from A to B.

10.A line has one end in HP and the other end in VP It is inclined at 30° to HP, and 45° to VP. Length of the line is 80 mm. Draw the three views of the line and measure the distance between the end projectors in the front view. How far the end A is infront of VP?

11.The midpoint of a line AB is 60 mm above HP and 50 mm infront of VP. The line measures 80 mm and is inclined at 30° to HP and 45° to VP. Draw its projections.

12.A line AB 90 mm long is inclined at 45° to HP and 30° to VP. A point C lies on the line such that it is 40 mm from A, and 60 mm above HP and 50 mm infront of VP. Obtain the projections of the line.

13.One end of a pole 2 metre long rests against a wall and the other on the top of a box. The box is 1 metre high. The pole makes 40° with the top of the box and 25° with the wall. Draw the projections and find the height of the end of the pole which rests against the wall. Scale 1m = 4 cm.

14.A line AB, 80 mm long has its end A in both HP and VP, and inclined at 30° to HP and 45° to VP. Draw its projections and traces.

15.A straight line PQ, 75mm long is inclined at 45° to HP and 30° to VP. The point P is 80 mm from the planes of projection and the point Q is nearer to the said planes. Draw the projections of the straight line.

16.A line PQ, 75 mm long has its end P in the VP and the end Q in the HP. The line is inclined at 30° to HP and 60° to VP. Draw its projections and traces.

True Length and True Inclinations

17.A line AB located in the first quadrant is 80 mm long. The end A is touching VP and 10 mm above HP. The end B is 50 mm infront of VPand 30 mm above HP. Draw the projections of AB and finds the distance between the end projectors when measured parallel to the line of intersection of HP and VP. Also find the inclination of the line with HP and VP.

18.A 5 metre pole rests with end A aginst a wall and the other end B resting on the ground. A is 2 m above the ground and B is 3 m away from the wall. Draw the top view and the front view to a scale of 1 m = 20 mm. Find the true inclinations of the pole with the wall and the ground.

19.The end A of a line AB is in HP and 25 mm infront of VP. The end B is in VP and 50 mm above HP. The distance between the end projectors when measured parallel to the line of intersection of HP and VP is 65 mm. Draw the projections of the line AB and determine its true length and true inclinations with HP and VP. Mark the traces.

20.A line has its end A, 15 mm from HP and 10 mm from VP. The end B is 55 mm from HP and the line is inclined at 30° to HP. The distance between the end projectors is 50 mm. Draw the projections of the line. Determine the true length of the line and its inclination with VP.

21.A line AB is 90 mm long. It is inclined at 45° to HP. Its front view measures 70 mm. The end A is 15 mm above HP and 25 mm infront of VP. The end B is in the first quadrant. Draw the projections of the line AB. Determine its traces, its inclination to VP and the length of its top view.

22.A line measuring 80 mm has one of its ends 40 mm infront of VP and 15 mm above HP and the other end is infront of VP and is 40 mm above HP. The front view of the line is 50 mm long. Draw the front view of the line and find the inclinations of the line with HP and VP.

23.The top view of a 75 mm long line CD measures 50 mm. The midpoint of the line is 50 mm from VP and 75 mm from the HP. The point D is 30 mm from VP. Draw its projections and find its inclinations with the HP and VP.

24.The top view of a line PQ, 75 mm long measures 50 mm. The end Pis 50 mm infront of VP and 15 mm above HP. The end Q is 15 mm infront VP and above HP. Draw the projections of the line PQ and find its true inclination with HP and VP.

25.The top view ab of a straight line AB is 60 mm long and it makes an angle of 30° with the XY line. The end A is in the VP and 30 mm above the HP. The end B is 65 mm above the HP. The line lies in the quadrant. Draw the projections of the line AB and determinethe length of the front view of the line AB, its true length, its tracesand its inclination with the reference planes.

26.A point Pis 40 mm above HP and 20 mm infront of VP. Another point Q is 20 mm above HP and 50 mm infront of VP. The top view of the line is inclined at 30° to the XY line. Draw the top and front views of the line. Find true length, traces on two the planesand inclinations with the two planes.

27.The top view pq of a straight line is 60 mm long and makes an angle of 60° with the XY line. The point Q is 10 mm infront of VP and 25 mm above HP. The difference between the distances of P and Q above the HP is 45 mm. Draw the projections. Determine its true length. Show the traces on HP and VP.

28.The front view of a line is 80 mm in length and makes 40° with the ground line. Its midpoint C is 60 mm infront of VP and 60 mm above HP. The point A is 50 mm infront of VP. Draw the top and front views of the line. Determine true length and inclinations of the line with the reference planes. Locate its traces.

29.The top and front views of a line are inclined at 35° and 50° to the XY line respectively. One end of the line is touching both HP and VP. The other end is 50 mm above HP and 30 mminfront VP. Find the true length, true inclinations of the line with HP and VP and mark thetraces.

30.The front view of a line AB, 125 mm long measures 85 mm, and its top view measures 100 mm. Its end B and the midpoint M are in the first quadrant. The midpoint M being 65 mm from both the planes. Draw the projection of the line AB and find the inclinations of the line with HP and VP.

31.The front view of a line AB measuring 125 mm long is 75 mm and its top view is 100 mm long. Its end B is 30 mm from both the planes. Draw the projections and find its inclinations and with the reference planes.

32.A line MY measures 120 mm. Its top and front views measure 80 mm and 96 mm respectively. A point Pon the line, dividing it in the ratio of 1: 2, i.e., MP: PN= 1:2, is at a distance of 80 mm from both the reference planes. Draw the projections of the line, and determine its traces and inclinations with the reference planes.

33.The top view of a line AB, 80 mm long measures 65 mm and the length of the front view is 50 mm. The end A is on HP and 15 mm infront of VP. Draw the projection of AB and determine its inclinations with HP and VP.

34.The top view of a line PQ is 70 mm long while its front view is 60 mm long. Q is nearer to HP than P, and Q is also nearer to VP than P. The distance between the ends projectors of the line when measured parallel to the line of intersection of HPand VP is 50 mm. Determine its true length, traces and inclinations with the reference planes.

35.AB is a straight line whose front view measures 60 mm and makes an angle of 45° with the XY line. The end A is in the HP and the vertical trace of the line is 10 mm below the HP. The straight line is inclined at 30° to VP. Draw the projections of the line AB and find its true length and true inclination with HP. Also locate its horizontal trace. How far the end A is from VP?

36.A line AB is in the first quadrant. Its ends A and B are 20 mm and 60 mm infront of VP respectively. The distance between the end projectors is 75 mm. The line is inclined at 30° to the HPand its horizontal trace is 10 mm below the XY line. Draw the projections of AB. determine its true length and the vertical trace.

37.One end of a line PQ is at a distance of 25 mm infront of VP and 30 mm above HP. The top view of the line measures 70 mm. The distance between the end projectors when measured parallel to the line of intersection of HP and VP is 50 mm, and the vertical trace is 10 mm above the line of intersection of HP and VP. Draw the projections of PQ. Find the true length of the line PQ and the true angles that the line PQ makes with HP and VP. Also locate the horizontal trace of line PQ.

38.The projectors through the traces of a line are 110 mm apart, and those through the ends of the line AB are 50 mm apart. The end A of the line is 20 mm above HP. The top and front views of the line make 30° and 40° with the XY line respectively. Draw the projections of the line and find the true length and true inclinations of the line. Find the shortest distance from the point A to the XY line.

39.The projectors drawn from the horizontal and vertical traces of a line AB are 112 mm apart and those drawn from the ends of a straight line AB are 30 mm apart. The horizontal trace is located 42 mm infront of VP and the vertical trace is 32 mm below HP. The end A of the line lies in HP. Draw the top and front views of the line. Determine its true length and inclinations with the planes of projection.

40.A line PQ measuring 150 mm has its vertical trace 15 mm above the horizontal plane. The end P is 40 mm above the horizontal plane and 30 mm infront of the vertical plane. The projectors through its vertical trace and end Pare 60 mm apart. Determine the projections and the horizontal trace of the line. Also find its inclinations with the reference planes.

A point R is in the vertical plane 80 mm from the end P and 125 mm from the end Q of the above line PQ. Determine its distance from horizontal plane.

If the distance of the point R from P remains constant, and the points remain in the vertical plane, what is its least possible distance from Q?

41.A straight line AB150 mm long has its end A on the horizontal plane at a distance of 100 mm from the horizontal plane, and 45 mm from the Vertical plane. It is parallel to the vertical plane and inclined to the horizontal plane at 30°. Now it is slowly turned about the end A keeping the inclination with the horizontal plane constant, so that the end B just touches the Vertical plane. Draw the projections of AB in this position and determine the true inclination of AB with the Vertical plane.

42.A straight line AB measuring 160 mm long has its vertical trace 80 mm above the XY line and the horizontal trace 100 mm infront of XY line. The projections of the HTand VT on the XY line are 200 mm apart. If the point A is 10 mm above HP. Draw the projections of AB in all the three views and find its true angles of inclinations with respect to HP and VP. Select a Scale 1:2.

43.ABC is an equilateral triangle of 70 mm sides. A is in HP and B is in VP. Side AB is inclined at 450 to HP and 30° to VP. Side BC is inclined at 350 to HP. Draw the top and front views of the triangle and find the inclinations of the side AC with HP.

44.A divider opened at 450is so placed on the ground such that both the ends are equidistant front the VP and the hinged end is 50 mm above the ground. If the distance between the ends is 80 mm. Draw the projections and determine the true lengths of thelegs of the divider. Also determine the inclinations of each leg with the reference planes.

45.A room is 5 m long, 4 m wide and 4 m high. A fan is suspended vertically from the centre of the ceiling at a distance of 0.75 m from it. Find the distance of the fan from any one of the ground corners and the slope angle of the connecting line with the ground.

46.A room is 6m x 5m x 3.5m high. An object is placed 1.2m above the ground and in the centre of the room. Determine graphically its distance from one of the corners between the roof and the adjacent walls. Select a Scale 1:50.

47.A room is 5m x 4m x 3m high. Determine graphically the length of the diagonal of the space choosing a suitable scale

48.An auditorium of a college is having 100m length, 50m width and 20m maximum height. A light point is fitted at the centre of the roof, and its switch is kept on one of the side walls of the auditorium 1.5 m above the floor and 10 m from one of the adjacent wall. Find the distance between the light point and its switch.

49.Two pegs A and B are fixed one in each of the adjacent walls of a rectangular room. Peg A is 1m above the floor4 m from the side wall and its protruding 0.3m from the wall on which it is fixed. Peg B is 2.5 m above the floor1.5m from the wall on which the Peg A is fixed and is also protruding 0.3m from the wall on which it is fixed. Find the distance between the ends of the pegs.

50.Two nails A and B are driven one in each of the adjacent walls of a room measuring 3.5m x 5m x 4m high. Nail A driven on 5m wall, is 3m above thefloor and 2m from the left adjacent wall. Nail B is driven on the right adjacent wall at the centre. Athird nail Cdriven on the ceiling, is 1m from the right adjacent wall and 2 m from the 5 m wall. It is desired to connect A and B to C by two wires. Find the total length of the wire required, neglecting the length required for tieing.

51.Two fan motors hang from the ceiling of a hall12m x 15m x 3m high at a height of 1 m from the ceiling. The motors are 3m and 9m from the 12 m wall, 2 m and 3 m from the 15 m wall. Determine graphically the distance of each motor from a corner of the hall of the floor.

52.Three vertical poles AB, CD and EF are respectively 2m, 4m and 8m long. Their ends B, Dand Fare on the ground and form the corners of an equilateral triangle of 5 m long sides. Determine graphically the distances between the top ends of the poles, namely AC, CEand AE: also the inclination of these with the ground. Scale 1:50.

53.The top view of a tripod formed by a set of three bars supported at the apex on the top of a post, on the HP forms equiangular with one another, and of Y shape. The legs of Y are equal to 40 mm long and the angles between them are also equal.The top ends of these three bars are respectively at a height of 160 mm, 175 mm and 185 mm above the ground. The height of the post is 150 mm. Draw the projections of the tripod. Find the true length of each bar and inclinations with HP and VP.

54.A chimney of a boiler is 25 m high and 1 m in diameter. This chimney is supported by three guy wires which appear in top view at 120° to each other. The ends of the wires are pegged to the ground at distances of 3 m, 4 m and 5 m from the centre of the chimney. The other ends of the wire are connected to the top of the chimney. Find the length of the three guy wires.

55.A flag post O is 9 metre high. It is supported by three guy wires. The top ends of the wires are tied to the flag post and their lower ends are tied to the top of the three pegs. A, B and C fixed to the ground. The pegs A, Band C are 0.5 m, 0.75 m and 1 m high respectively. In the top view three guy wires appear to be at 120° to each other and the lengths of their top views are oa=3m, ob = 4m and oc = 5 m. Draw the projections of the guy wires and the pegs, and determine the true lengths of the guy wires and the true inclinations they make with the ground. Adopt a scale 1:100

56.A radio antenna mast DE is supported by three cables AD, BD and CD is shown in figure. It is desired that all the three cables shall make the same angle with the mast. Find (a) the true length and the angle with the mast of the cable AD, (b) what distance the anchorage B must be from the base of the mast and the true length of BD? (c) How far the given point C must be moved along the sloping ground towards or away from the mast, and the true length of CD after moving C.

57.Three guy ropes AB, CD and EF aretied at points A,Cand Eon avertical post 7.5m long at height of 7m, 6m and 5m respectively above the ground. The lower ends of the ropes are tied to hooks at points B, D and Fon ground. If the points B, D and Flie at the corners of an equilateral triangle of 4.5m sides and if the post is situated at the centre of this triangle, determine graphically the length of each rope and its inclination with the ground. Take the thickness of the post and the ropes as negligible.