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Byju's Answer
Standard X
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
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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 two lines
L
1
and
L
2
are given by
L
2
:
r
=
(
2
^
i
+
9
^
j
+
13
^
k
)
+
λ
(
^
i
+
2
^
j
+
3
^
k
)
and
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 vector equation of the plane through the point
^
i
+
2
^
j
−
^
k
and perpendicular to the line of intersection of the plane
¯
r
.
(
3
^
i
−
9
^
j
+
^
k
)
=
1
and
¯
r
.
(
^
i
+
4
^
j
−
2
^
k
)
=
2
is:
Q.
For component of vector
→
P
=
^
i
+
2
^
j
−
3
^
k
values are in column - II, then the correct match is:
Column I
Column II
a)
X-axis
p)
1
b)
Along vector
q)
√
14
→
q
=
^
i
+
2
^
j
+
5
3
^
k
c)
Along vector
r)
0
→
r
=
2
^
i
+
4
^
j
−
6
^
k
d)
Along vector
s)
√
7
→
s
=
^
i
+
2
^
j
−
3
^
k
√
14
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