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}. $