Given that P(3,2,-4), Q(5,4,-6) and R(9,8,-10) are collinear. Find the ratio in which Q divides PR.

Given that A (3, 2,-4), B(5, 4, -6) and C(9, 8, -10) are collinear. Find the ratio in which B divides [AC].

Show that the three points A(2,3,4) and B(-1,2,-3) and C(-4,1,-10) are collinear and find the ratio in which C divides [AB].

Using section formula, prove that the three points (-4,6,10), (2,4,6) and (14,0,-20) are collinear. Also find the ratio in which point B divides the join of A and C.

Show that the points A (1, - 2, - 8), B (5, 0,- 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Prove that the ponts A(1,2,3),B(3,4,7),C(-3 ,-2, -5) are collinear and find the ratio in which B divides AC.

Show that the points P(2,6),Q(1,2)and R(3,10) are collinear.

The points P=(1,2), Q = (2, 4) and R=(4,8) form a/an:

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. [Hint Suppose R divides PQ in the ratio k :1. The coordinates of the point R are given by ((8k+2)/(k+1), (-3)/(k+1), (10k+4)/(k+1)) .

If the origin is the centroid of the triangle PQR with vertices P(2a,2,6), Q(-4,3b,-10) and R(8,14,2c), then find the value of a,b and c.