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.

Given: A(1, – 2, – 8), B(5, 0, –2) and C(11, 3, 7)

Then

Then

Thus the given points are collinear.

Now to find the ratio in which B divides AC. Let it be λ :1

On equating the terms, we get:

5(λ + 1) = 11λ + 1

⇒ 5λ + 5 = 11λ + 1

⇒ 4 = 6λ

⇒ λ = 4/6 = 2/3

Hence, B divides AC in the ratio 2:3.

10