Question

The image of the point $(3,-1,11)$ w.r.t the line $\frac{x}{{}^2}=\frac{y-2}{3}=\frac{z-3}{4}$ is

Answer 1

REF.Image.

General point (B) on the line

can be donated by

$\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\lambda$

$\Rightarrow x=2\lambda ,y=3\lambda +2,z=4\lambda +3$

$\Rightarrow \overrightarrow{AB}=(2\lambda +3)\hat{i}+(3\lambda +3)\hat{j}+(4\lambda -8)\hat{k}$

As $\overrightarrow{AB}\perp l\Rightarrow \overrightarrow{AB}.l=0$

$\Rightarrow (2\lambda -3,3\lambda +3,4\lambda -8).(2,3,4)=0$

$\Rightarrow 4\lambda -6+9\lambda +9+16\lambda -32=0$

$\Rightarrow 29\lambda =29\Rightarrow \lambda =1$

$\Rightarrow B(-1,6,-4)$

As B is mid - point of AC, $\Rightarrow c(-2,3,12+1,-8-11)=(-5,13,-19)$