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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
a’
X Y
a
b’
b 1
b 1 ’
b 2 ’
b 2
Φ β
TL
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
X
Y
a’
b 1 ’
a
b 2
70
30 °
45 °
b 1
b
b’
b 2 ’
h’
HT
v
VT’
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
b 1
Hint: Draw ab 1 =65mm // to XY. Because when TV is // to XY, FV gives TL.
b’ b 1 ’
65
b
b 2
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
Ans. θ=31º
Ans. Ø=49º
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 50 Y
a’
a
b
b’
b 1
Ans. θ=20º
b 2 ’
b 2
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.
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.
X Y
a’
a
b 1 ’
b 1 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
b 2
Ans. Ø = 38º
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 12 Y
a’
a
30 °
b 1 ’
b’
b 1
b
90
b 2
44 °
Ans: Ø = 44º
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’
b^ a
120 ° a’
c
120 °
c 1
c 1 ’
c 2
c 2 ’
112 °
C
Ans. 112º
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
b’
a’
VT’
h’
b 2 ’
40 º^ v
b 2
a
b 1
b 1 ’
21 º HT
Ans, TL = 85 mm, θ = 21º & HT is 17 mm behind VP
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
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
d 1
d 1 ’ d’
Ø=48º
Ans: Ø=48º
d 2
75
θ=28º
Ans: θ=28º
