JEE Main 2023 (Online) 30th January Evening ShiftQuestion 1
Let a line $L$ pass through the point $P(2,3,1)$ and be parallel to the line $x+3y-2z-2=0=x-y+2z$. If the distance of $L$ from the point $(5,3,8)$ is $\alpha$, then $3\alpha^{2}$ is equal to
3D Geometry
Answer$158$
Solution
Direction $=(1,3,-2)\times(1,-1,2)\parallel(1,-1,-1)$. With $\vec{PQ}=(3,0,7)$, $\vec{PQ}\times d=(7,10,-3)$, so $\alpha^2=\frac{158}{3}$ and $3\alpha^2=158$.