For three vectors $\to u, \to v, \to w$ which of the following expressions is not equal to any of remaining is

\to u . (\to v \times \to w)

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(\to v \times \to w) . \to u

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\to v . (\to u \times \to w)

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(\to u \times \to v) . \to w

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Solution

The correct option is D $\to v . (\to u \times \to w)$
In a scalar triple product dot and cross can be interchanged.
$\to u . (\to v \times \to w) = (\to u \times \to v) . \to w$
the vectors can be changed cyclically.
$∴ (\to v \times \to w) . \to u = (\to u \times \to v) . \to w$
$\Rightarrow \to v . (\to u \times \to w) = - \to u . (\to v \times \to w)$

Suggest Corrections

u, v

w

z^{3} - 1 = 0

u . v + v . w + w . u

\to u, \to v, \to w

\to u, \to v

\to w

(\to u + \to v - \to w) . (\to u - \to v) \times (\to v - \to w)

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