JEE Main 2020 (Online) 4th September Evening ShiftQuestion 1
If $\vec a=2\hat i+\hat j+2\hat k$, then the value of $\left|\hat i\times(\vec a\times\hat i)\right|^2+\left|\hat j\times(\vec a\times\hat j)\right|^2+\left|\hat k\times(\vec a\times\hat k)\right|^2$ is equal to ________.
Vector Algebra
Answer$18$
Solution
$\hat i\times(\vec a\times\hat i)=\vec a-(\vec a\cdot\hat i)\hat i$, the component of $\vec a$ perpendicular to $\hat i$; its squared length is $|\vec a|^2-a_x^2$. Sum $=3|\vec a|^2-|\vec a|^2=2|\vec a|^2=2\cdot9=18$.