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Joint Entrance Examination
Mathematics
Vector Algebra
Question 330
Question 330 of 379
Medium
MCQ
Let
a
⃗
=
i
^
+
j
^
+
k
^
\vec a=\hat i+\hat j+\hat k
a
=
i
^
+
j
^
+
k
^
,
b
⃗
=
i
^
−
j
^
+
2
k
^
\vec b=\hat i-\hat j+2\hat k
b
=
i
^
−
j
^
+
2
k
^
and
c
⃗
=
x
i
^
+
(
x
−
2
)
j
^
−
k
^
\vec c=x\hat i+(x-2)\hat j-\hat k
c
=
x
i
^
+
(
x
−
2
)
j
^
−
k
^
. If the vector
c
⃗
\vec c
c
lies in the plane of
a
⃗
\vec a
a
and
b
⃗
\vec b
b
, then
x
x
x
equals:
A
−
4
-4
−
4
B
−
2
-2
−
2
C
0
0
0
D
1
1
1
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Official solution
\[\begin{vmatrix}1&1&1\\1&-1&2\\x&x-2&-1\end{vmatrix}=0 \implies [1-2(x-2)]-[-1-2x]+[x-2+x]=0\] \[1-2x+4+1+2x+2x-2=0 \implies 2x=-4 \implies x=-2\]
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