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Mathematics
Problem
If vectors
a
=
i
^
+
2
j
^
−
k
^
\mathbf{a} = \hat{i} + 2\hat{j} - \hat{k}
a
=
i
^
+
2
j
^
−
k
^
,
b
=
2
i
^
−
j
^
+
k
^
\mathbf{b} = 2\hat{i} - \hat{j} + \hat{k}
b
=
2
i
^
−
j
^
+
k
^
and
c
=
λ
i
^
+
j
^
+
2
k
^
\mathbf{c} = \lambda\hat{i} + \hat{j} + 2\hat{k}
c
=
λ
i
^
+
j
^
+
2
k
^
are coplanar, then find the value of
(
λ
−
4
)
(\lambda - 4)
(
λ
−
4
)
.
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