IIT-JEE 2002 ScreeningQuestion 1
If $\vec a$ and $\vec b$ are two unit vectors such that $\vec a+2\vec b$ and $5\vec a-4\vec b$ are perpendicular to each other then the angle between $\vec a$ and $\vec b$ is
Vector Algebra
Solution
$(\vec a+2\vec b)\cdot(5\vec a-4\vec b)=5+6\,\vec a\cdot\vec b-8=0$, so $\cos\theta=\tfrac12$ and $\theta=60^\circ$.