If the points $A(-1,0,7), B(3,2, t), C(5, k,-2)$ are collinear, then the ratio in which the point $P(t, k-2t, t+k)$ divides the line segment $BC$ is

If coordinates of the points $A$ and $B$ are $(2, 4)$ and $(4, 2)$ respectively and point $M$ is such that $A-M-B$ and $AB = 3AM$,then the coordinates of $M$ are

The harmonic conjugate of $(2,3,4)$ with respect to the points $(3,-2,2)$ and $(6,-17,-4)$ is

If the centroid of a tetrahedron $OABC$ is $(1, 2, -1)$, where $O$ is the origin, $A(a, 2, 3)$, $B(1, b, 2)$, and $C(2, 1, c)$ are the other vertices, then the distance of the point $P(a, b, c)$ from the origin is...

If $A(1, 2, 0)$,$B(2, 0, 1)$,and $C(-3, 0, 2)$ are the vertices of $\triangle ABC$,then the length of the internal bisector of $\angle BAC$ is

If $A(4,7,8)$, $B(2,3,4)$, and $C(2,5,7)$ are the vertices of $\triangle ABC$, then the length of the internal bisector of the angle $A$ is