Question

The direction ratios of `bar"AB"` are - 2, 2, 1. If A ≡ (4, 1, 5) and l(AB) = 6 units, find B.

Answer 1

The direction ratio of `bar"AB"` are -2, 2, 1.

∴ the direction cosines of `bar"AB"` are

l = `(- 2)/sqrt((- 2)^2 + 2^2 + 1^2) = (-2)/3`,

m = `2/sqrt((- 2)^2 + 2^2 + 1^2) = 2/3`,

n = `1/sqrt((- 2)^2 + 2^2 + 1^2) = 1/3`.

i.e. l = `(-2)/3`, m = `2/3`, n = `1/3`

The coordinates of the points which are at a distance of d units from the point (x₁, y₁, z₁) are given by (x₁ ± ld, y₁ ± md, z₁ ± nd)

Here, x₁ = 4, y₁ = 1, z₁ = 5, d = 6, l = `-2/3`, m = `2/3`, n = `1/3`

∴ the coordinates of the required points are

`(4 +- (- 2/3)6, 1 +- 2/3(6), 5 +- 1/3(6))`

i.e. (4 - 4, 1 + 4, 5 + 2) and (4 + 4, 1 - 4, 5 - 2)

i.e. (0, 5, 7) and (8, - 3, 3).