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Mathematics
Mathematics
Problem
If
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
are vectors in space given by
a
⃗
=
i
^
−
2
j
^
5
\vec{a} = \frac{\hat{i} - 2\hat{j}}{\sqrt{5}}
a
=
5
i
^
−
2
j
^
and
b
⃗
=
2
i
^
+
j
^
+
3
k
^
14
\vec{b} = \frac{2\hat{i} + \hat{j} + 3\hat{k}}{\sqrt{14}}
b
=
14
2
i
^
+
j
^
+
3
k
^
, then the value of
(
2
a
⃗
+
b
⃗
)
⋅
[
(
a
⃗
×
b
⃗
)
×
(
a
⃗
−
2
b
⃗
)
]
(2\vec{a} + \vec{b}) \cdot [(\vec{a} \times \vec{b}) \times (\vec{a} - 2\vec{b})]
(
2
a
+
b
)
⋅
[(
a
×
b
)
×
(
a
−
2
b
)]
is
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