The position vectors of points A, B and C are and respectively. If C divides the lien segment joining A and B in the ratio 3 : 1, find the values of λ and μ.

Let the position vectors of points A, B and C be, and respectively.

Given:, and

C divides AB internally in the ratio 3:1.

Recall the position vector of point P which divides AB, the line joining points A and B with position vectors and respectively, internally in the ratio m : n is

Here, m = 3 and n = 1.

We have, and

By comparing both sides, we get 36 + λ = –44

⇒ λ = –44 – 36

∴ λ = –80

We also have 3μ + 3 = –12

⇒ 3μ = –15

∴ μ = –5

Thus, λ = –80 and μ = –5