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Dot Product of Two Vectors

Let a=î+ĵ+k̂ ...

Question

Let $\to a =^i +^j +^k$ and $\to b =^j -^k .$ If $\to c$ is a vector such that $\to a \times \to c = \to b$ and $\to a \cdot \to c = 3,$ then $\to a \cdot (\to b \times \to c)$ is equal to

A

6

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B

- 2

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C

- 6

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D

2

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Solution

The correct option is B $- 2$
$\to a \cdot (\to b \times \to c) = (\to b \times \to c) \cdot \to a = \to b \cdot (\to c \times \to a)$
$= \to b \cdot (- \to b) [∵ \to a \times \to c = \to b]$
$= - | \to b |^{2}$
$= - (1^{2} + (- 1)^{2}) = - 2$

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