If the planes $x + 2y + kz = 0$ and $2x + y - 2z = 0$ are at right angles,then the value of $k$ is

Find the equation of the plane passing through the points $A(2, 2, -1)$,$B(3, 4, 2)$,and $C(7, 0, 6)$.

If ${P_1}$ and ${P_2}$ are the lengths of the perpendiculars from the points $(2, 3, 4)$ and $(1, 1, 4)$ respectively to the plane $3x - 6y + 2z + 11 = 0$,then ${P_1}$ and ${P_2}$ are the roots of the equation:

$P$ and $Q$ are points on the straight line passing through the point $A(3 \hat{i}+\hat{j}-\hat{k})$ and parallel to the vector $\vec{v} = 2 \hat{i}-\hat{j}+2 \hat{k}$. If $AP = AQ = 3$,then the vector equation of the plane $OPQ$ is:

The image of the point $(1, 2, -1)$ on the plane containing the line $\frac{x + 1}{-3} = \frac{y - 3}{2} = \frac{z + 2}{1}$ and the point $(0, 7, -7)$ is:

The equation of a plane passing through $(-1, 2, 3)$ and whose normal makes equal angles with the coordinate axes is