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Subtraction of a Vector

If a×b ×c=a× ...

Question

If $(\to a \times \to b) \times \to c = \to a \times (\to b \times \to c)$ where $\to a, \to b$ and $\to c$ are three non-zero vectors such that $\to a \cdot \to b \neq 0, \to b \cdot \to c \neq 0,$ then $\to a$ and $\to c$ are

A

inclined at an angle of

\frac{π}{3}

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B

inclined at an angle of

\frac{π}{6}

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C

perpendicular

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D

parallel

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Solution

The correct option is D parallel
$(\to a \times \to b) \times \to c = \to a \times (\to b \times \to c)$
$\Rightarrow (\to a \cdot \to c) \to b - (\to b \cdot \to c) \to a = (\to a \cdot \to c) \to b - (\to a \cdot \to b) \to c$ $\Rightarrow (\to a \cdot \to b) \to c = (\to b \cdot \to c) \to a$
$∴ \to a$ is parallel to $\to c$

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Subtraction of a Vector

Standard XII Physics

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