JEE Main 2017 (Offline)Question 1
If the image of the point $P(1,-2,3)$ in the plane $2x+3y-4z+22=0$ measured parallel to the line $\frac x1=\frac y4=\frac z5$ is $Q$, then $PQ$ is equal to :
3D Geometry
Solution
Line $P+s(1,4,5)$ meets the plane when $2(1+s)+3(-2+4s)-4(3+5s)+22=6-6s=0$, so $s=1$. Image is at $2s$: $PQ=2|(1,4,5)|=2\sqrt{42}$.