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Byju's Answer
Standard X
Mathematics
Point of Intersection of Two Lines
The lines r...
Question
The lines
→
r
=
→
a
+
λ
(
→
b
×
→
c
)
and
→
r
=
→
b
+
μ
(
→
c
×
→
a
)
will intersect if
(
→
a
,
→
b
,
→
c
are non-coplanar
)
A
→
a
×
→
c
=
→
b
×
→
c
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B
→
a
.
→
c
=
→
b
.
→
c
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C
→
b
×
→
a
=
→
c
×
→
a
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D
None of these
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Solution
The correct option is
B
→
a
.
→
c
=
→
b
.
→
c
The lines
→
r
=
→
a
+
λ
(
→
b
×
→
c
)
and
→
r
=
→
b
+
μ
(
→
c
×
→
a
)
pass through points
→
a
and
→
b
respectively.
Therefore, they intersect if
→
a
−
→
b
,
→
b
×
→
c
and
→
c
×
→
a
are coplanar and so
(
→
a
−
→
b
)
.
(
(
→
b
×
→
c
)
×
(
→
c
×
→
d
)
)
=
0
⇒
(
→
a
−
→
b
)
.
[
(
→
b
→
c
→
a
)
→
c
−
(
→
b
→
c
→
c
)
→
a
]
=
0
⇒
(
(
→
a
−
→
b
)
.
→
c
)
[
→
b
→
c
→
a
]
=
0
(
∵
→
a
,
→
b
,
→
c
are non-coplanar
)
⇒
→
a
.
→
c
=
→
b
.
→
c
⇒
[
→
b
→
c
→
a
]
≠
0
Suggest Corrections
0
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