The locus of a first degree equation in $x, y, z$ is a

Find the angle between the planes $\vec{r} \cdot (2\hat{i} - \hat{j} + \hat{k}) = 6$ and $\vec{r} \cdot (\hat{i} + \hat{j} + 2\hat{k}) = 5$.

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

The foot of the perpendicular drawn from the origin to a plane is $M(2, 1, -2)$. Find the vector equation of the plane.

The equation of a plane parallel to the plane $x - 2y + 2z - 5 = 0$ and at a unit distance from the origin is:

The coordinates of the points $A$ and $B$ are $(2, 3, 4)$ and $(-2, 5, -4)$ respectively. If a point $P(x, y, z)$ moves such that $PA^2 - PB^2 = k$,where $k$ is a constant,then the locus of $P$ is: