JEE Main 2023 (Online) 1st February Evening ShiftQuestion 1
Let $\vec a=2\hat i-7\hat j+5\hat k$, $\vec b=\hat i+\hat k$ and $\vec c=\hat i+2\hat j-3\hat k$ be three given vectors. If $\vec r$ is a vector such that $\vec r\times\vec a=\vec c\times\vec a$ and $\vec r\cdot\vec b=0$, then $|\vec r|$ is equal to :
Vector Algebra
Solution
$(\vec r-\vec c)\times\vec a=0$, so $\vec r=\vec c+t\vec a$. $\vec r\cdot\vec b=-2+7t=0$, $t=\frac27$, $\vec r=(\frac{11}7,0,-\frac{11}7)$ and $|\vec r|=\frac{11\sqrt2}7$.