Let be three unit vectors such that is not parallel to , then the angle between is

Engineering

Mathematics

Vector Triple Product

Question

Let $\vec{a}, \vec{b} and \vec{c}$ be three unit vectors such that $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\sqrt{3}}{2} (\vec{b} + \vec{c}) . if \vec{b}$ is not parallel to $\vec{c}$ , then the angle between $\vec{a} and \vec{b}$ is

$\frac{5 π}{6}$

$\frac{2 π}{3}$

$\frac{3 π}{4}$

$\frac{π}{2}$

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$\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\sqrt{3}}{2} (\vec{b} + \vec{c})$

$\Rightarrow (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c} = \frac{\sqrt{3}}{2} \vec{b} + \frac{\sqrt{3}}{2} \vec{c}$

$∴ \vec{a} \cdot \vec{b} = \frac{- \sqrt{3}}{2} \Rightarrow \cos θ = \frac{- \sqrt{3}}{2}$

$\Rightarrow θ = \frac{5 π}{6} .$