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Projection of straight line Line inclined to both HP & VP Type-I Given projections (FV & TV) of the line. To find True length & true inclination of the line with HP (θ) and with VP(Φ). End A of a line AB is 15mm above HP & 20mm in front of VP while its end B is 50mm above HP and 75mm in front of VP. The distance between end projectors of the line is 50mm. Draw projections of the line and find its true length and true inclination with the principal planes. Also mark its traces. PROBLEM

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a’ X Y a 15 20 50 b’ 75 b1b1 b1’ b1’ b 2 ’ b2 b2 θ α Φβ TLTL TL h’ HT v VT’ b θ: True inclination of the line with HP = 24º α : Inclination of FV of the line with HP/XY Ø: True inclination of the line with VP = 41º β : Inclination of TV of the line with VP/XY

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Type –II Given (i) T.L., θ and Ø, (ii) T.L., F.V., T.V. to draw projections, find α, β,H.T. and V.T. Line inclined to both HP & VP PROBLEM A line AB, 70mm long, has its end A 15mm above HP and 20mm in front of VP. It is inclined at 30° to HP and 45°to VP. Draw its projections and mark its traces.

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X Y 15 a’ 20 70 b1’b1’ a b2b2 30° 45° b1b1 b b’ b2’b2’ h’ HT v VT’

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Q10.11 The top view of a 75mm long line AB measures 65mm,while its front view measures 50mm. Its one end A is in HP and12mm in front of VP. Draw the projections of AB and determine its inclination with HP and VP X Y a’ 12 a b1b1 Hint: Draw ab 1 =65mm // to XY. Because when TV is // to XY, FV gives TL. 75 b1’b1’ b’ 50 65 b 75 b2b2 Given, TL=75mm,TV=65mm,FV=50mm A is in HP & 12mm → VP To draw FV &TV of the line AB To find θ & Ø 31º 49º Ans. θ=31º Ans. Ø=49º

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Q10.12 A line AB, 65mm long has its end A 20mm above H.P. and 25mm in front of VP. The end B is 40mm above H.P. and 65mm in front of V.P. Draw the projections of AB and show its inclination with H.P. and V.P. X Y 20 a’ 25 a 40 65 Given, TL=65mm A is 20mm ↑ HP & 25mm → V.P. B is 40mm ↑ & 65mm → V.P. To draw FV &TV of the line AB To find θ & Ø Hint1:Mark a’ 20mm above H.P & a 25mm below XY Hint2:Draw locus of b’ 40mm above XY & locus of b 65 mm below XY 65 b1’b1’ b1b1 b b’ b2’b2’ b2b2 65 18º 38º Ans. θ=18º Ans. Ø=38º

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Q10.13: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 V.P. The end B is1cm below H.P. and 4cm behind the V.P. Determine the true length and traces of AB, and its inclination with the two planes X Y 50 20 a’ 30 a 40 b 10 b’ b1b1 91 Ans. θ=20º 20º b2’b2’ b2b2 50º Ans. Ø=50º h’ HT v VT’ Given, A 0 B 0 =50mm A is 20mm ↑ HP & 30mm → V.P. B is 10mm ↓ & 40mm ← V.P. To find, True Length, θ,Ø, H.T. and V.T.

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Q10.14:A line AB, 90mm long, is inclined at 45 to the H.P. and its top view makes an angle of 60 with the V.P. The end A is in the H.P. and 12mm in front of V.P. Draw its front view and find its true inclination with the V.P. Y X a’ a 12 90 45º b1’b1’ b1b1 60º b b’ Given, T.L.=90mm, θ=45º, β=60º A is in the H.P. & 12mm→V.P. To find/draw, F.V.,T.V. & Ø 90 b2b2 38º Ans. Ø = 38º

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Q10.16:The end A of a line AB is 25 mm behind the V.P. and is below the H.P. The end B is 12 mm in front of the VP and is above the HP The distance between the projectors is 65mm. The line is inclined at 40 to the HP and its HT is 20 mm behind the VP. Draw the projections of the line and determine its true length and the VT X Y Given, A 0 B 0 =65mm A is 25mm ←V.P.& is ↓ H.P. B is 12mm →V.P. & is above HP θ = 40º To find/draw, F.V., T.V., T.L., VT’ 25 a 65 12 b 20 HT h’ b1b1 40º b1’b1’ b’ a’ v VT’ b2b2 b2’b2’

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10.17:A line AB, 90mm long, is inclined at 30 to the HP. Its end A is 12mm above the HP and 20mm in front of the VP. Its FV measures 65mm. Draw the TV of AB and determine its inclination with the VP X Y 12 a’ 20a 90 30° b1’b1’ 65 b’ b1b1 b 90 b2b2 44° Ans: Ø = 44º

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Q10.23:Two lines AB & AC make an angle of 120 between them in their FV & TV. AB is parallel to both the HP & VP. Determine the real angle between AB & AC. X Y c’ b’ a b a’ 120° c c1c1 c1’c1’ c2c2 c2’c2’ 112° C Ans. 112º

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Q8:A line AB 65 mm long has its end A in the H.P. & 15 mm infront of the V.P.The end B is in the third quadrant. The line is inclined at 30 to the H.P. and at 60 to the V.P. Draw its projections.

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Q10.19 A line AB, inclined at 40º to the V.P. has its end 50mm and 20mm above the H.P. the length of its front view is 65mm and its V.T. is 10mm above the H.P. determine.the true length of AB its inclination with the H.P. and its H.T. Given, Ø = 40º, A is 20mm↑HP, B is 50 mm ↑ HP, FV=65mm, VT is 10mm ↑ HP To find, TL, θ & HT X Y 50 b’ 20 a’ 10 VT’ h’ b2’b2’ v 40º b2b2 b a b1b1 b1’b1’ 85 21º HT Ans, TL = 85 mm, θ = 21º & HT is 17 mm behind VP

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Q6. The top view of a 75mm long line CD measures 50 mm. C is 50 mm in front of the VP & 15mm below the HP. D is 15 mm in front of the VP & is above the HP. Draw the FV of CD & find its inclinations with the HP and the VP. Show also its traces. X Y 15 50 Given, TL = 75 mm, FV =50 mm, C is 15mm ↓ HP & 50 mm → VP, D is 15 mm → VP To draw, FV & to find θ & Ø c’ c Locus of D Hint 1: Cut anarc of 50 mm from c on locus of D d Hint 2: Make TV (cd), // to XY so that FV will give TL d1d1 d1’d1’ d’ Ø=48º Ans: Ø=48º d2d2 50 75 θ=28º Ans: θ=28º

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Q10.10 A line PQ 100 mm long is inclined at 30º to the H.P. and at 45º to the V.P. Its mid point is in the V.P. and 20 mm above the H.P. Draw its projections, if its end P is in the third quadrant and Q is in the first quadrant. Given, TL = 100, θ = 30º, Mid point M is 20mm↑HP & in the VP End P in third quadrant & End Q in first quadrant To draw, FV & TV X Y 20 m’ m 30º q1’q1’ p1’p1’ 50 q2q2 p2p2 q2’q2’ q’ p’ q p q2q2 p1p1 p2’p2’

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