In what ratio does the $yz$-plane divide the line segment joining the points $(-2, 4, 7)$ and $(3, -5, 8)$?

If $Q(\alpha, \beta, \gamma)$ is the harmonic conjugate of the point $P(0, -7, 1)$ with respect to the line segment joining the points $A(2, -5, 3)$ and $B(-1, -8, 0)$,then $\alpha - \beta + \gamma =$

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 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

In what ratio does the $x$-axis divide the line segment joining the points $(3, 4)$ and $(5, 6)$?

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