Question

Let $OABC$ 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

• A. 0
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{5}{6}$

Answer 1

Answer: (C)

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