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

Locate the following points in a three-dimensional Cartesian coordinate system:
$(i)$ $(1, -1, 3)$
$(ii)$ $(-1, 2, 4)$
$(iii)$ $(-2, -4, -7)$
$(iv)$ $(-4, 2, -5)$

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.

Which of the following is at a distance of $\sqrt{10}$ from the point $(1, 2, 3)$?

Let $A, B, C$ be the feet of the perpendiculars from a point $P$ on the $xy, yz,$ and $zx$-planes respectively. Find the coordinates of $A, B, C$ for the following points $P$:
$(3, 4, 5), (-5, 3, 7), (4, -3, -5)$

The point on the $X$-axis which is equidistant from $A\ (2, -5, 7)$ and $B\ (1, 3, 6)$ is . . . . . . .