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Joint Entrance Examination
Mathematics
3D Geometry
Question 456
Question 456 of 521
Medium
MCQ
The two lines
x
=
a
y
+
b
,
z
=
c
y
+
d
;
x=ay+b, z=cy+d;
x
=
a
y
+
b
,
z
=
cy
+
d
;
and
x
=
a
′
y
+
b
′
,
x=a'y+b' ,
x
=
a
′
y
+
b
′
,
z
=
c
′
y
+
d
′
z=c'y+d'
z
=
c
′
y
+
d
′
are perpendicular to each other if :
A
\[aa'+cc'=-1\]
B
\[aa'+cc'=1\]
C
\[{a \over {a'}} + {c \over {c'}} = - 1\]
D
\[{a \over {a'}} + {c \over {c'}} = 1\]
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Official solution
Equation of lines \[{{x - b} \over a} = {y \over 1} = {{z - d} \over c}\] \[{{x - b'} \over {a'}} = {y \over 1} = {{z - d'} \over {c'}}\] Line are perpendicular \[ \Rightarrow aa' + 1 + cc' = 0\]
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