JEE Main 2021 (Online) 16th March Morning ShiftQuestion 1
Let $P$ be a plane $lx+my+nz=0$ containing the line, $\dfrac{1-x}{1}=\dfrac{y+4}{2}=\dfrac{z+2}{3}$. If plane $P$ divides the line segment $AB$ joining points $A(-3,-6,1)$ and $B(2,4,-3)$ in ratio $k:1$ then the value of $k$ is equal to :
3D Geometry
Solution
The plane passes through the origin and $(1,-4,-2)$ and contains direction $(-1,2,3)$: $l-4m-2n=0$, $-l+2m+3n=0$ give $(l,m,n)\propto(8,1,2)$. Plane $8x+y+2z=0$; value at $A$ is $-28$, at $B$ is $14$, so $k=28/14=2$.