Question

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.

• A. 1:2
• B. 1:3
• C. 1:4
• D. 2:3

Answer 1

Answer: (A)

1:2

Let Q divide PR in the ratio k:1. Equate the x-coordinate of the point of division to 5.

$\therefore \frac{3+9k}{k+1}=53+9k=5k+54k=2k=\frac{1}{2}$

Since it is given that P, Q and R are collinear, we need to calculate k only for any one of the coordinates.