The ratio in which the straight line $3x + 4y = 6$ divides the join of the points $(2, -1)$ and $(1, 1)$ is

Two particles $P$ and $Q$ located at the points with coordinates $P(t, t^3-16t-3)$ and $Q(t+1, t^3-6t-6)$ are moving in a plane. The minimum distance between them in their motion is

The coordinates of the point dividing internally the line segment joining the points $(4, -2)$ and $(8, 6)$ in the ratio $7 : 5$ are:

If the polar coordinates of a point are $\left(\sqrt{2}, \frac{\pi}{4}\right)$,then its Cartesian coordinates are

If the line $2x - 3y + 4 = 0$ divides the line segment joining the points $A(-2, 3)$ and $B(3, -2)$ in the ratio $m:n$,then the point which divides $AB$ in the ratio $-4m:3n$ is

If the points $A(6, -1)$,$B(1, 3)$ and $C(x, 8)$ are such that $AB = BC$,then $x = $