If the line joining $A(1,3,4)$ and $B$ is divided by the point $P(-2,3,5)$ in the ratio $1:3$,then the coordinates of $B$ are:

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 the point $(3,4,5)$ divides the line segment joining the points $(1,2,3)$ and $(4,5,6)$ in the ratio $\lambda: 1$,then the point which divides the line segment joining the points $(3,4,5)$ and $(1,2,3)$ in the ratio $-1: \lambda$ is

If $P=(3,12,4)$ and $Q$ is a point on the line $OP$ such that $OQ=3$,then the sum of all the coordinates of $Q$ is

Find the ratio in which the line segment joining the points $(4, 8, 10)$ and $(6, 10, -8)$ is divided by the $YZ$-plane.

If the orthocenter and circumcenter of a triangle are $(3, -4, 2)$ and $(2, 1, 3)$ respectively,then its centroid is