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Multiplication with Vectors

For three vec...

Question

For three vectors $\to u, \to v, \to w$ which of the following expressions is no equal to any one of the remaining three option?

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is C $\to v \cdot (\to u \times \to w)$
First, dot product is commutative and thus $\to a \cdot \to b = \to b \cdot \to a$
Also, scalar triple product is cyclic and so $[\to a \to b \to c] = [\to b \to c \to a] = [\to c \to a \to b]$
Using these, we have option c as the answer.

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