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: P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) and P, Q and R are collinear

To find: the ratio in which Q divides PR

Formula used:

Section Formula:

A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).

The coordinates of C is given by,

Let Q divides PR in ratio k : 1

Therefore, m = k and n = 1

P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10)

Coordinates of Q using section formula:

On comparing:

⇒ 9k + 3 = 5(k + 1)

⇒ 9k + 3 = 5k + 5

⇒ 9k – 5k = 5 – 3

⇒ 4k = 2

Q divides PR externally in ratio 1:2