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Mathematics
Mathematics
Problem
Let
a
=
α
i
^
+
2
j
^
−
3
k
^
\mathbf{a} = \alpha\hat{i} + 2\hat{j} - 3\hat{k}
a
=
α
i
^
+
2
j
^
−
3
k
^
,
b
=
i
^
+
2
α
j
^
−
2
k
^
\mathbf{b} = \hat{i} + 2\alpha\hat{j} - 2\hat{k}
b
=
i
^
+
2
α
j
^
−
2
k
^
and
c
=
2
i
^
−
α
j
^
+
k
^
\mathbf{c} = 2\hat{i} - \alpha\hat{j} + \hat{k}
c
=
2
i
^
−
α
j
^
+
k
^
. Then the value of
6
α
6\alpha
6
α
, such that
{
(
a
×
b
)
×
(
b
×
c
)
}
×
(
c
×
a
)
=
0
,
is
\left\{(\mathbf{a} \times \mathbf{b}) \times (\mathbf{b} \times \mathbf{c})\right\} \times (\mathbf{c} \times \mathbf{a}) = 0, \text{ is}
{
(
a
×
b
)
×
(
b
×
c
)
}
×
(
c
×
a
)
=
0
,
is
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