JEE Main 2026 (Online) 2nd April Morning ShiftQuestion 1
If $\vec a$ and $\vec b$ are two vectors such that $|\vec a|=2$ and $|\vec b|=3$, then the maximum value of $3\left|\left(3\vec a+2\vec b\right)\right|+4\left|\left(3\vec a-2\vec b\right)\right|$ is :
Vector Algebra
Solution
Let $u=|3\vec a+2\vec b|$, $v=|3\vec a-2\vec b|$. Then $u^2+v^2=2(36+36)=144$. By Cauchy-Schwarz, $3u+4v\le5\sqrt{144}=60$, attainable for a suitable angle.