The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the $XY$-plane is:

If $(2, -1, 3)$ is the foot of the perpendicular drawn from the origin $(0, 0, 0)$ to a plane,then the equation of that plane is:

Let the points on the plane $P$ be equidistant from the points $A(-4, 2, 1)$ and $B(2, -2, 3)$. Then the acute angle between the plane $P$ and the plane $2x + y + 3z = 1$ is

Find the distance of the point $(0, 0, 0)$ from the plane $3x - 4y + 12z = 3$. (in $/13$)

If $M$ denotes the midpoint of the line segment joining $A(4, 5, -10)$ and $B(-1, 2, 1)$, then the equation of the plane passing through $M$ and perpendicular to $AB$ is:

The equation $axy + byz = cy$ represents the locus of the points which lie on