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Condition for Two Lines to be on the Same Plane

Let a, b ,c...

Question

Let $\to a, \to b, \to c$ be non-coplanar vectors such that $\to a \times (\to b \times \to c) = \frac{\to b}{2}$ , then the angle between $\to a$ and $\to b$ is

A

\frac{3 π}{4}

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B

\frac{π}{4}

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C

\frac{π}{2}

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D

π

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Solution

The correct option is C $\frac{π}{2}$
$\to a \times (\to b \times \to c) = \frac{\to b}{2}$ (given)
$\Rightarrow (\to a . \to c) \to b - (\to a . \to b) \to c = \frac{\to b}{2}$
$\Rightarrow \to a . \to b = 0, (\to a . \to c) \to b = \frac{\to b}{2}$
$\Rightarrow \to a . \to c = \frac{1}{2}$
$∴ \to a ⊥ \to b$

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