The equation of the plane bisecting the line segment joining the points $(2,0,6)$ and $(-6,2,4)$ and perpendicular to it,is

The equation of the plane passing through the points with position vectors $A(2 \hat{i}+6 \hat{j}-6 \hat{k})$,$B(-3 \hat{i}+10 \hat{j}-9 \hat{k})$ and $C(-5 \hat{i}-6 \hat{k})$ is

If a plane passes through $(1, -2, 1)$ and is perpendicular to the planes $2x - 2y + z = 0$ and $x - y + 2z = 4$,then the distance of that plane from the point $(1, 2, 2)$ is

Find the equation of a plane,given that the foot of the perpendicular drawn to the plane from the origin is $(2, 1, 2)$.

If the angle between the planes $\vec{r} \cdot(m \hat{i}-\hat{j}+2 \hat{k})+3=0$ and $\vec{r} \cdot(2 \hat{i}-m \hat{j}+\hat{k})-5=0$ is $\frac{\pi}{3}$,then $m=$

If the angle between the planes $ax - y + 3z = 2a$ and $3x + ay + z = 3a$ is $\frac{\pi}{3}$,then the direction ratios of the line perpendicular to the plane $(a+2)x + (a-4)y + 2az = a$ are