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Byju's Answer
Standard XII
Mathematics
Condition That 2 Lines Are Coplanar
The value of ...
Question
The value of p for which the straight lines
→
r
=
(
2
^
i
+
9
^
j
+
13
^
k
)
+
t
(
^
i
+
2
^
j
+
3
^
k
)
and
→
r
=
(
−
3
^
i
+
7
^
j
+
p
^
k
)
+
s
(
−
^
i
+
2
^
j
−
3
^
k
)
are coplanar is
A
-1
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B
1
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C
-2
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D
2
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Solution
The correct option is
C
-2
∣
∣ ∣
∣
5
2
13
−
p
1
2
3
−
1
2
−
3
∣
∣ ∣
∣
=
0
gives p = - 2
Suggest Corrections
0
Similar questions
Q.
The value of p for which the straight lines
→
r
=
(
2
^
i
+
9
^
j
+
13
^
k
)
+
t
(
^
i
+
2
^
j
+
3
^
k
)
and
→
r
=
(
−
3
^
i
+
7
^
j
+
p
^
k
)
+
s
(
−
^
i
+
2
^
j
−
3
^
k
)
are coplanar is
Q.
The value of p for which the straight lines
→
r
=
(
2
^
i
+
9
^
j
+
13
^
k
)
+
t
(
^
i
+
2
^
j
+
3
^
k
)
and
→
r
=
(
−
3
^
i
+
7
^
j
+
p
^
k
)
+
s
(
−
^
i
+
2
^
j
−
3
^
k
)
are coplanar is
Q.
The vector equations of the two lines
L
1
and
L
2
are given by
L
1
:
→
r
=
2
^
i
+
9
^
j
+
13
^
k
+
λ
(
^
i
+
2
^
j
+
3
^
k
)
;
L
2
:
→
r
=
−
3
^
i
+
7
^
j
+
p
^
k
+
μ
(
−
^
i
+
2
^
j
−
3
^
k
)
then the lines
L
1
and
L
2
are
Q.
The shortest distance between the skew lines
→
r
=
(
^
i
+
2
^
j
+
3
^
k
)
+
t
(
^
i
+
3
^
j
+
2
^
k
)
and
→
r
=
(
4
^
i
+
5
^
j
+
6
^
k
)
+
t
(
2
^
i
+
3
^
j
+
^
k
)
is
Q.
If the shortest distance between the lines
→
r
=
^
i
+
2
^
j
+
3
^
k
+
λ
(
2
^
i
+
3
^
j
+
4
^
k
)
and
→
r
=
2
^
i
+
4
^
j
+
5
^
k
+
μ
(
3
^
i
+
4
^
j
+
5
^
k
)
is
k
, then the value of
tan
−
1
tan
(
2
√
6
k
)
is
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