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Q.

If $\vec{a}, \vec{b} and \vec{c}$ are three mutually orthogonal unit vectors, then the triple product $[\vec{a} + \vec{b} + \vec{c} \vec{a} + \vec{b} \vec{b} + \vec{c}]$ equals

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a

1 or -1

b

1

c

0

d

3

answer is B.

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Detailed Solution

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Here $[\vec{a} \vec{b} \vec{c}] = \pm 1$

$\begin{array}{l} = (\vec{a} + \vec{b} + \vec{c}) \times (\vec{a} + \vec{b}) \cdot (\vec{b} + \vec{c}) \\ = \vec{c} \times (\vec{a} + \vec{b}) \cdot (\vec{b} + \vec{c}) \\ = (\vec{c} \times \vec{a} + \vec{c} \times \vec{b}) \cdot (\vec{b} + \vec{c}) \\ = \vec{c} \times \vec{a} \cdot \vec{b} = [\vec{a} \vec{b} \vec{c}] = \pm 1 \end{array}$

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