IIT-JEE 2002 ScreeningQuestion 1
Let $\vec V=2\hat i+\hat j-\hat k$ and $\vec W=\hat i+3\hat k$. If $\vec U$ is a unit vector, then the maximum value of the scalar triple product $\left|[\vec U\ \vec V\ \vec W]\right|$ is
Vector Algebra
Solution
$|[\vec U\,\vec V\,\vec W]|=|\vec U\cdot(\vec V\times\vec W)|\le|\vec V\times\vec W|$ with $\vec V\times\vec W=3\hat i-7\hat j-\hat k$, magnitude $\sqrt{59}$, attained when $\vec U$ is along it.