If the points $A(1, 3, 5)$, $B(2, 4, 6)$, and $C(4, 5, k)$ form a right-angled triangle, then the number of possible values of $k$ is:

In a triangle $ABC$, if the midpoints of sides $AB, BC, CA$ are $(3,0,0), (0,4,0), (0,0,5)$ respectively, then $AB^2+BC^2+CA^2=$

Let $A(2, 2, -3)$,$B(5, 6, 9)$,and $C(2, 7, 9)$ be the vertices of a triangle. The angle bisector of $\angle A$ meets $BC$ at the point $D$. Find the coordinates of $D$.

If $P(0, 7, 10)$,$Q(-1, 6, 6)$,and $R(-4, 9, 6)$ are three points in space,then $\triangle PQR$ is:

If the coordinates of the points $A, B, C$ are $(-1, 3, 2)$,$(2, 3, 5)$,and $(3, 5, -2)$ respectively,then $\angle A = \dots^o$.

Verify that the points $(0, 7, -10)$,$(1, 6, -6)$,and $(4, 9, -6)$ are the vertices of an isosceles triangle.