If $A(1, 2, 3)$ and $B(-1, -1, -1)$ are two points,then the distance $AB$ is:

If the coordinates of points $A$ and $B$ are $(3, 4, 5)$ and $(-1, 3, -7)$ respectively,find the equation of the locus of point $P(x, y, z)$ such that $PA^2 - PB^2 + 2k^2 = 0$.

The distance between the points $(1, 3, 2)$ and $(2, 1, 3)$ is:

The sum of the squares of the perpendicular distances of a point $(x, y, z)$ from the coordinate axes is $k$ times the square of the distance of the point from the origin. Then $k=$

Show that the points $(-2, 3, 5), (1, 2, 3),$ and $(7, 0, -1)$ are collinear.

Find the equation of the set of points $P$ such that $PA^{2} + PB^{2} = 2k^{2}$,where $A$ and $B$ are the points $(3, 4, 5)$ and $(-1, 3, -7)$,respectively.