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

Answer 1

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

Let the required plane be $a(x–1)+b(y–1)+c(z–1)=0$
Direction ratio of its normal is
$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 1& -2\\ 3& -6& -2\end{array}\right|=-14\hat{i}-2\hat{j}-15\hat{k}$

$\therefore$ Equation of the plane is $-14(x–1)-2(y–1)-15(z–1)=0\Rightarrow 14x+2y+15z=31$