JEE Main 2022 (Online) 26th July Morning ShiftQuestion 1
The length of the perpendicular from the point $(1,-2,5)$ on the line passing through $(1,2,4)$ and parallel to the line $x+y-z=0=x-2y+3z-5$ is :
3D Geometry
Solution
Direction: $(1,1,-1)\times(1,-2,3)=(1,-4,-3)$. Vector from $(1,2,4)$ to $(1,-2,5)$: $v=(0,-4,1)$. $v\times d=\big((-4)(-3)-(1)(-4),\;(1)(1)-0,\;0-(-4)(1)\big)=(16,1,4)$, magnitude$^2=273$; $|d|^2=26$. $p^2=\frac{273}{26}=\frac{21}{2}$, so $p=\sqrt{21/2}$. Option (A).