JEE Main 2021 (Online) 26th February Evening ShiftQuestion 1
Let $L$ be a line obtained from the intersection of two planes $x+2y+z=6$ and $y+2z=4$. If point $P(\alpha,\beta,\gamma)$ is the foot of perpendicular from $(3,2,1)$ on $L$, then the value of $21(\alpha+\beta+\gamma)$ equals :
3D Geometry
Solution
Direction $(1,2,1)\times(0,1,2)=(3,-2,1)$, point $(-2,4,0)$. Foot of $(3,2,1)$: $14t-20=0$, $t=\frac{10}7$, foot $(\frac{16}7,\frac87,\frac{10}7)$. $21\cdot\frac{34}7=102$.