Question

The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes
$2x+y–2z=5\text{and}3x–6y–2z=7$, is

• A. $14x+2y+15z=31$
• B. $–14x+2y+15z=3$
• C. $14x+2y–15z=1$
• D. $14x–2y+15z=27$

Answer 1

The correct option is A $14x+2y+15z=31$

Required equation of plane is
$\left|\begin{array}{ccc}x-1& y-1& z-1\\ 2& 1& -2\\ 3& -6& -2\end{array}\right|=0$
$\Rightarrow –14(x–1)–2(y–1)+(–15)(z–1)=0$
$\Rightarrow 14x+2y+15z=31$