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Mathematics
Problem
Let
a
⃗
=
i
^
+
2
j
^
+
4
k
^
\vec{a} = \hat{i} + 2\hat{j} + 4\hat{k}
a
=
i
^
+
2
j
^
+
4
k
^
,
b
⃗
=
i
^
+
λ
j
^
+
4
k
^
\vec{b} = \hat{i} + \lambda\hat{j} + 4\hat{k}
b
=
i
^
+
λ
j
^
+
4
k
^
and
c
⃗
=
2
i
^
+
4
j
^
+
(
λ
2
−
1
)
k
^
\vec{c} = 2\hat{i} + 4\hat{j} + (\lambda^2 - 1)\hat{k}
c
=
2
i
^
+
4
j
^
+
(
λ
2
−
1
)
k
^
be coplanar vectors. Then the non-zero vector
a
⃗
×
c
⃗
\vec{a} \times \vec{c}
a
×
c
is : [JEE-MAIN ONLINE-2019] (1)
−
14
i
^
−
5
j
^
-14\hat{i} - 5\hat{j}
−
14
i
^
−
5
j
^
(2)
−
10
i
^
−
5
j
^
-10\hat{i} - 5\hat{j}
−
10
i
^
−
5
j
^
(3)
−
10
i
^
+
5
j
^
-10\hat{i} + 5\hat{j}
−
10
i
^
+
5
j
^
(4)
−
14
i
^
+
5
j
^
-14\hat{i} + 5\hat{j}
−
14
i
^
+
5
j
^
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