JEE Main 2021 (Online) 27th July Morning ShiftQuestion 1
Let a plane $P$ pass through the point $(3,7,-7)$ and contain the line $\frac{x-2}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$. If distance of the plane $P$ from the origin is $d$, then $d^2$ is equal to ________.
3D Geometry
Answer$3$
Solution
Point on the line $A(2,3,-2)$, direction $(-3,2,1)$; $P=(3,7,-7)$. $\overrightarrow{AP}=(1,4,-5)$. Normal $=\overrightarrow{AP}\times(-3,2,1)=(14,14,14)\parallel(1,1,1)$. Plane: $x+y+z=2+3-2=3$. Check: $3+7-7=3$. $d=\dfrac{3}{\sqrt3}$, so $d^2=3$.