Distance Formula in 3D

Verify whether the four points $\left(5, -1, 1\right), \left(-1, -3, 4\right),$ $\left(7, -4, 7\right)$ and $\left(1, -6, 10\right)$ are the vertices of rhombus or not.

Show that the points $\left(0, 7, 10\right), \left(-1, 6, 6\right)$ and $\left(-4, 9, 6\right)$ form a right angled triangle.

The points (5, -4, 2), (4, -3, 1), (7, -6, 4) and (8, -7, 5) are the vertices of

The points $A\left(5,-1,1\right), B\left(7,-4,7\right), C\left(1,-6,10\right)$ and $D\left(-1,-3,4\right)$ are vertices of a

The perpendicular distance of the point $\left(6, 5, 8\right)$ from $y$-axis is

If the coordinate of the verities of a triangle $ABC$ be $A\left(-\mathrm{1,3},2\right), B\left(\mathrm{2,3},5\right) \&\mathrm{ }C\left(\mathrm{3,5},-2\right),$ then $\angle A$ is equal to

The distance between the points $\left(1,4,5\right)$ and $\left(2,2,3\right)$ is

A point on $x$-axis which is equidistant from both the points $\left(1,2,3\right)$ and $(3,5,-2)$ is

The point equidistant from the point ($a, 0, 0$), $\left(0, b, 0\right),(0, 0, c)$ and $\left(0,0,0\right)$ is