Question

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

• A. $3x-10y-2z+11=0$
• B. $6x-5y-2z-2=0$
• C. $11x+y+17z+38=0$
• D. $6x-5y+2z+10=0$

Answer 1

The correct option is C $11x+y+17z+38=0$

$\because$ Required plane is perpendicual to both the planes
$\therefore$Normal vector of required plane is
$\overrightarrow{n}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 1& -2\\ 2& -5& -1\end{array}\right|$
$\overrightarrow{n}=-11\hat{i}-\hat{j}-17\hat{k}$
Hence eqaution of required plane will be
$-11(x-1)-(y-2)-17(z+3)=0$
$\Rightarrow 11x+y+17z+38=0$