JEE Main Solved Paper 2017 Question 22
Question: If the image of the point P(1,-2,3) in the plane, $ 2x+3y-4z+22=0 $ measured parallel to line, $ \frac{x}{1}=\frac{y}{4}=\frac{z}{5} $ is Q, then PQ is equal to:- [JEE Main Solved Paper-2017]
Options:
A) $ 6\sqrt{5} $
B) $ 3\sqrt{5} $
C) $ 2\sqrt{42} $
D) $ \sqrt{42} $
Show Answer
Answer:
Correct Answer: C
Solution:
Line $ PQ:\frac{x-1}{1}=\frac{y+2}{4}=\frac{z-3}{5} $
Let $ F(\lambda +1,4\lambda -2,5\lambda +3) $
F lies on the plane $ 2(\lambda +1)+3(4\lambda -2)-4(5\lambda +3)+22=0 $
$ \Rightarrow $ $ -6\lambda +6=0\Rightarrow \lambda =1 $ $ F(2,2,8) $ $ PQ=2,PF=2\sqrt{42}. $
