Let \(\vec{\alpha}=\hat{i}+\hat{j}+\hat{k}, \vec{\beta}=\hat{i}-\hat{j}-\hat{k}\) and \(\vec{\gamma}=-\hat{i}+\hat{j}-\hat{k}\) be three vectors. A vector \(\vec{\delta}\), in the plane of \(\vec{\alpha}\) and \(\vec{\beta}\), whose projection on \(\vec{\gamma}\) is \(\frac{1}{\sqrt{3}}\), is given by

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Let \(\vec{\alpha}=\hat{i}+\hat{j}+\hat{k}, \vec{\beta}=\hat{i}-\hat{j}-\hat{k}\) and \(\vec{\gamma}=-\hat{i}+\hat{j}-\hat{k}\) be three vectors. A vector \(\vec{\delta}\), in the plane of \(\vec{\alpha}\) and \(\vec{\beta}\), whose projection on \(\vec{\gamma}\) is \(\frac{1}{\sqrt{3}}\), is given by

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kritika · Answer 1 · 2021-12-27T07:23:45+0000

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

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