# The equation of the plane passing

Question:

The equation of the plane passing through the point $(1,2,-3)$ and perpendicular to the planes $3 x+y-2 z=5$ and $2 x-5 y-z=7$, is:

1. (1) $3 x-10 y-2 z+11=0$

2. (2) $6 x-5 y-2 z-2=0$

3. (3) $11 x+y+17 z+38=0$

4. (4) $6 x-5 y+2 z+10=0$

Correct Option: , 3

Solution:

Normal vector of required plane is $\vec{n}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 3 & 1 & -2 \\ 2 & -5 & -1\end{array}\right|=-11 \hat{i}-\hat{j}-17 \hat{k}$

$\therefore 11(x-1)+(y-2)+17(z+3)=0$

$11 x+y+17 z+38=0$