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Joint Entrance Examination
Mathematics
Vector Algebra
Question 320
Question 320 of 379
Medium
MCQ
If
a
⃗
=
i
^
−
2
j
^
+
3
k
^
\vec a=\hat i-2\hat j+3\hat k
a
=
i
^
−
2
j
^
+
3
k
^
,
b
⃗
=
2
i
^
+
3
j
^
−
k
^
\vec b=2\hat i+3\hat j-\hat k
b
=
2
i
^
+
3
j
^
−
k
^
and
c
⃗
=
λ
i
^
+
j
^
+
(
2
λ
−
1
)
k
^
\vec c=\lambda\hat i+\hat j+(2\lambda-1)\hat k
c
=
λ
i
^
+
j
^
+
(
2
λ
−
1
)
k
^
are coplanar vectors, then
λ
\lambda
λ
is equal to:
A
0
0
0
B
−
1
-1
−
1
C
2
2
2
D
1
1
1
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Official solution
\[\begin{vmatrix}1&-2&3\\2&3&-1\\\lambda&1&2\lambda-1\end{vmatrix}=0 \implies (6\lambda-2)+2(5\lambda-2)+(6-9\lambda)=0 \implies 7\lambda=0 \implies \lambda=0\]
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