Question

Let \(\vec{\alpha}, \vec{\beta}, \vec{\gamma}\) be three unit vectors such that \(\vec{\alpha} \cdot \vec{\beta}=\vec{\alpha} \cdot \vec{\gamma}=0\) and the angle between \(\vec{\beta}\) and \(\vec{\gamma}\) is \(30^{\circ}\). Then \(\vec{\alpha}\) is
(A) \(2(\vec{\beta} \times \vec{\gamma})\)
(B) \(-2(\vec{\beta} \times \vec{\gamma})\)
(C) \(\pm 2(\vec{\beta} \times \vec{\gamma})\)
(D) \((\vec{\beta} \times \vec{\gamma})\)

Answer 1

Ans: (C)
Hint \(: \vec{\alpha}=\lambda(\vec{\beta} \times \vec{\gamma}) \Rightarrow|\vec{\alpha}|=|\lambda(\vec{\beta} \times \vec{\gamma})| \Rightarrow 1=|\lambda||\beta||\gamma| \sin 30^{\circ} \Rightarrow|\lambda|=2 \Rightarrow \lambda=\pm 2\)

Answer 2

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Answer 3

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