Question

Find the value of λ for which the points (6, – 1, 2), (8, – 7, λ) and (5, 2, 4) are collinear.

Answer 1

Let A(6, – 1, 2), B(8, – 7, λ) and C(5, 2, 4) be the given points.

Then direction ratios of line AB are

8 – 6, – 7 – (– 1), λ – 2, i.e. 2, – 6, λ – 2

and direction ratios of line AC are

5 – 6, 2 – (– 1), 4 – 2, i.e. – 1, 3, 2

Since A, B, C are collinear, the direction ratios of AB and AC are in the same proportion.

∴ `2/-1 = (-6)/3 = (λ - 2)/2`

∴ – 2 = `(λ - 2)/2`

∴ – 4 = λ – 2

∴ λ = – 2