# If the equation of plane passing through

Question:

If the equation of plane passing through the mirror image of a point $(2,3,1)$ with respect to line $\frac{x+1}{2}=\frac{y-3}{1}=\frac{z+2}{-1}$ and containing the line $\frac{x-2}{3}=\frac{1-y}{2}=\frac{z+1}{1}$ is $\alpha x+\beta y+\gamma z=24$ then $\alpha+\beta+\gamma$ is equal to :

1. (1) 20

2. (2) 19

3. (3) 18

4. (4) 21

Correct Option: , 2

Solution:

$\therefore$ Reflection $(-2,4,-6)$ Plane : $\left|\begin{array}{ccc}\mathrm{x}-2 & \mathrm{y}-1 & \mathrm{z}+1 \\ 3 & -2 & 1 \\ 4 & -3 & 5\end{array}\right|=0$

$\Rightarrow(x-2)(-10+3)-(y-1)(15-4)+(z+1)(-1)=0$

$\Rightarrow-7 x+14-11 y+11-z-1=0$

$\Rightarrow 7 x+11 y+z=24$

$\therefore \alpha=7, \beta=11, \gamma=1$

$\alpha+\beta+\gamma=19$