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 equal to

• A. -1
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (B)

Line is $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}=\lambda :$ Let point $R$ is
$(2\lambda -1,-2\lambda +3,-\lambda )$
Direction ratio of $PQ\equiv (2\lambda -2,-2\lambda +1,3-\lambda )$
$PO$ is ${\perp }^r$ to line
$\Rightarrow 2(2\lambda -2)-2(-2\lambda +1)-1(3-\lambda )=0$
$4\lambda -4+4\lambda -2-3+\lambda =0$
$9\lambda =9\Rightarrow \lambda =1$
$\Rightarrow$ Point R is $(1,1,-1)$
$\begin{array}{c}\frac{a+1}{2}=1\\ a=1\end{array}\left|\begin{array}{c}\frac{b+2}{2}=1\\ b=0\end{array}\right|\begin{array}{c}\frac{c-3}{2}=-1\\ c=1\end{array}$
$\Rightarrow a+b+c=2$