question_answer

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

A)  \[6\sqrt{5}\]                                     

B)  \[3\sqrt{5}\]

C)  \[2\sqrt{42}\]                  

D)  \[\sqrt{42}\]

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                 \[2(\lambda +1)+3(4\lambda -2)-4(5\lambda +3)+22=0\]                 \[\Rightarrow \]\[-6\lambda +6=0\Rightarrow \lambda =1\]                 \[F(2,2,8)\]                 \[PQ=2\,PF=2\sqrt{42}.\]