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  4. Let O A B C be a regular tetrahedron of side length unity, where O is origin. If P is a point at a unit distance from origin such that OP is equally inclined to OA , OB and OC at an angle α. Then cos 2 α equals

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Q. Let $O A B C$ be a regular tetrahedron of side length unity, where $O$ is origin. If $P$ is a point at a unit distance from origin such that $OP$ is equally inclined to $\overrightarrow{ OA }, \overrightarrow{ OB }$ and $\overrightarrow{ OC }$ at an angle $\alpha$. Then $\cos ^2 \alpha$ equals

Vector Algebra

Solution:

Correct answer is (c) $ \frac{2}{3}$

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