Q2 of 25 Page 277

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.

Let Q divides PR in the ratio k : 1.

By Section Formula,


We know that the coordinates of the point R which divides the line segment joining two points P (x1, y1, z1) and Q (x2, y2, z2) internally in the ratio m : n is given by:



Comparing this information with the details given in the question, we have


x1 = 3, y1 = 2, z1 = -4; x2 = 9, y2 = 8, z2 = -10 and m = k, n = 1


So, we have




⇒ 9k + 3 = 5 (k+1) ⇒ 9k + 3 = 5k + 5 ⇒ 4k = 2



Hence, the ratio in which Q divides PR is 1 : 2.


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