JEE Main 2020 (Online) 9th January Evening ShiftQuestion 1
Let $\vec a,\vec b$ and $\vec c$ be three vectors such that $|\vec a|=\sqrt3$, $|\vec b|=5$, $\vec b\cdot\vec c=10$ and the angle between $\vec b$ and $\vec c$ is $\frac\pi3$. If $\vec a$ is perpendicular to the vector $\vec b\times\vec c$, then $\left|\vec a\times(\vec b\times\vec c)\right|$ is equal to ________.
Vector Algebra
Answer$30$
Solution
$\vec b\cdot\vec c=5|\vec c|\cos60^\circ=10\Rightarrow|\vec c|=4$. $|\vec b\times\vec c|=5\cdot4\sin60^\circ=10\sqrt3$. $\vec a\perp(\vec b\times\vec c)\Rightarrow|\vec a\times(\vec b\times\vec c)|=\sqrt3\cdot10\sqrt3=30$.