IIT-JEE 1981Question 1
State TRUE or FALSE: Let $\vec A,\vec B$ and $\vec C$ be unit vectors. Suppose that $\vec A\cdot\vec B=\vec A\cdot\vec C=0$, and that the angle between $\vec B$ and $\vec C$ is $\pi/6$. Then $\vec A=\pm2\left(\vec B\times\vec C\right)$.
Vector Algebra
Solution
$\vec A\perp\vec B,\vec C$ so $\vec A\parallel\vec B\times\vec C$, with $|\vec B\times\vec C|=\sin\frac\pi6=\frac12$. $\vec A$ is a unit vector, so $\vec A=\pm2(\vec B\times\vec C)$: TRUE.