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
Correct Option: , 2
Solution:
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 $\mathrm{PQ}=(2 \lambda-2,-2 \lambda+1,3-\lambda)$ $P Q$ is $\perp^{r}$ to line
$\Rightarrow 2(2 \lambda-2)-2(-2 \lambda+1)-1(3-\lambda)=0$
$4 \lambda-4+4 \lambda-2-3+\lambda=0$
$9 \lambda=9 \Rightarrow \lambda=1$
$\Rightarrow \quad$ Point $\mathrm{R}$ is $(1,1,-1)$
$\Rightarrow a+b+c=2$
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