$A$ point $R$ with $x$-coordinate $4$ lies on the line segment joining the points $P(2, -3, 4)$ and $Q(8, 0, 10)$. Find the coordinates of the point $R$.

If $A(1,2,3), B(2,-3,1), C(3,2,-1)$ are three vertices of a tetrahedron $ABCD$ and $G\left(\frac{5}{2}, \frac{3}{2}, \frac{9}{4}\right)$ is its centroid, then the point which divides $GD$ in the ratio $1:2$ is

The ratio in which the $yz$-plane divides the line segment joining $(-3, 4, -2)$ and $(2, 1, 3)$ is

The ratio in which the $yz$-plane divides the line segment joining the points $(-3, 4, -2)$ and $(2, 1, 3)$ is:

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

The ratio in which the point $P$,whose abscissa is $3$,divides the line segment joining $A(6, 5)$ and $B(-1, 4)$ is equal to .........