# The direction ratios of ABAB¯ are - 2, 2, 1. If A ≡ (4, 1, 5) and l(AB) = 6 units, find B. - Mathematics and Statistics

Sum

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

#### Solution

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).

Concept: Vector Product of Vectors (Cross)
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