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Applications of Cross Product

Given three u...

Question

Given three unit vectors $\to a, \to b, \to c$ ; no two of which collinear satisfying $\to a \times (\to b \times \to c) = \frac{1}{2} \to b$ . The angle between $\to a$ and $\to b$ is

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Solution

Given that,
$\begin{matrix} \to a \times (\to b \times \to c) = \frac{\to b}{2} (\to a \times \to c) \to b - (\to a \times \to b) \to c = \frac{\to b}{2} \Rightarrow \to a \times \to b = 0 \to a ⊥ \to b θ = 90^{0} \end{matrix}$
Then,
We get the angle between $\to a$ and $\to b$ is $90^{0}$ .

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