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Mathematics
Problem
Let
a
⃗
=
2
i
^
+
3
j
^
−
k
^
\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}
a
=
2
i
^
+
3
j
^
−
k
^
and
b
⃗
=
i
^
−
2
j
^
+
3
k
^
\vec{b} = \hat{i} - 2\hat{j} + 3\hat{k}
b
=
i
^
−
2
j
^
+
3
k
^
. Then the value of
λ
\lambda
λ
for which the vector
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
^
is parallel to the plane containing
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
, is- (A) 1 (B) 0 (C) -1 (D) 2
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