The equation of the $yz$-plane is

If the equation of the plane bisecting the line segment joining the points $P(3,2,4)$ and $Q(-1,0,-2)$ and perpendicular to $PQ$ is $ax+by+cz+d=0$,then find the value of $ac+bd$.

The vector equation of the plane passing through the point $2\hat{i} - \hat{j} - 4\hat{k}$ and parallel to the plane $\vec{r} \cdot (4\hat{i} - 12\hat{j} - 3\hat{k}) - 7 = 0$ is:

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x + 6y - 3z = 63$ are

If the foot of the perpendicular drawn from the origin to a plane is $P(2,-1,4)$,then the equation of the plane is

Find the angle between the two planes $3x - 6y + 2z = 7$ and $2x + 2y - 2z = 5$.