JEE Main 2021 (Online) 27th July Evening ShiftQuestion 1
The distance of the point $P(3,4,4)$ from the point of intersection of the line joining the points $Q(3,-4,-5)$ and $R(2,-3,1)$ and the plane $2x+y+z=7$, is equal to ________.
3D Geometry
Answer$7$
Solution
Line $QR$: $(3-t,\,-4+t,\,-5+6t)$. Plane: $2(3-t)+(-4+t)+(-5+6t)=7\Rightarrow -3+5t=7\Rightarrow t=2$. Intersection point $(1,-2,7)$. Distance from $P(3,4,4)$: $\sqrt{4+36+9}=7$.