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Byju's Answer
Standard XIII
Mathematics
Condition for Two Lines to Be Perpendicular
If the lines ...
Question
If the lines
x
=
a
y
+
b
,
z
=
c
y
+
d
and
x
=
a
′
z
+
b
′
,
y
=
c
′
z
+
d
′
are perpendicular, then :
A
a
b
′
+
b
c
′
+
1
=
0
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B
b
b
′
+
c
c
′
+
1
=
0
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C
a
a
′
+
c
+
c
′
=
0
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D
c
c
′
+
a
+
a
′
=
0
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Solution
The correct option is
C
a
a
′
+
c
+
c
′
=
0
Consider the lines
x
=
a
y
+
b
,
z
=
c
y
+
d
⇒
x
−
b
a
=
y
1
=
z
−
d
c
∴
→
b
1
=
a
^
i
+
^
j
+
c
^
k
Now,
x
=
a
′
z
+
b
′
,
y
=
c
′
z
+
d
′
⇒
x
−
b
′
a
′
=
y
−
d
′
c
′
=
z
1
∴
→
b
2
=
a
′
^
i
+
c
′
^
j
+
^
k
The two lines are perpendicular.
So,
→
b
1
⋅
→
b
2
=
0
⇒
a
a
′
+
c
′
+
c
=
0
Suggest Corrections
1
Similar questions
Q.
If the lines
x
=
a
y
+
b
,
z
=
c
y
+
d
and
x
=
a
′
z
+
b
′
,
y
=
c
′
z
+
d
′
are perpendicular, then :
Q.
The lines
x
=
a
y
+
b
and
z
=
c
y
+
d
and
x
=
a
′
y
+
b
′
and
z
=
c
′
y
+
d
will be perpendicular, if and only if
Q.
If the line
x
=
a
y
+
b
,
z
=
c
y
+
d
and the line
x
=
a
′
y
+
b
′
,
z
=
c
′
y
+
d
′
are perpendicular then :
Q.
The two lines
x
=
a
y
+
b
,
z
=
c
y
+
d
and
x
=
a
′
y
+
b
′
,
z
=
c
′
y
+
d
′
are perpendicular to each other if
Q.
The lines
x
=
a
y
+
b
,
z
=
c
y
+
d
,
x
=
a
′
y
+
b
′
,
z
=
c
′
y
+
d
′
are perpendicular if
a
a
′
+
c
c
′
equal to
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