AIEEE 2012 (Offline) 29th April Code AQuestion 1
Let $\hat a$ and $\hat b$ be two unit vectors. If the vectors $\vec c=\hat a+2\hat b$ and $\vec d=5\hat a-4\hat b$ are perpendicular to each other, then the angle between $\hat a$ and $\hat b$ is :
Vector Algebra
Solution
$(\hat a+2\hat b)\cdot(5\hat a-4\hat b)=5-4\hat a\cdot\hat b+10\hat a\cdot\hat b-8=6\hat a\cdot\hat b-3=0$, so $\cos\theta=\frac12$, $\theta=\frac\pi3$.