Question

If $(a,b,c)$ is the image of the point $(1,2,-3)$ in the line, $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1},$ then $a+b+c$ is

• A. $2$
• B. $3$
• C. $-1$
• D. $1$

Answer 1

The correct option is A $2$


$\overrightarrow{PM}\perp (2\hat{i}-2\hat{j}-\hat{k})$
$\Rightarrow (2\lambda -2)2+(1-2\lambda )(-2)+(3-\lambda )(-1)=0$
$\Rightarrow 4\lambda -4+4\lambda -2+\lambda -3=0$
$\Rightarrow 9\lambda =9\Rightarrow \lambda =1$
$\Rightarrow M(1,1,-1)$
Now, $P^{\prime }=2M-P$
$=2(1,1,-1)-(1,2,-3)$
$=(1,0,1)$
$\therefore a+b+c=2$