Sum

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

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#### Solution

The direction ratios of `bar"AB"` are −2, 2, 1

Let l, m, n be the direction cosines of AB.

∴ 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`

Now, A ≡ (4, 1, 5) and `|bar"AB"|` = 6 .......[Given]

If B ≡ (x, y, z), then

x – 4 = `+-(-2/3)|bar"AB"|`

y – 1 = `+- 2/3|bar"AB"|`

z – 5 = `+- 1/3|bar"AB"|`

∴ x = `4 +- (-2/3)(6)`

∴ x = 0 or x = 8

y = `1 +- 2/3 (6)`

∴ y = 5 or y = – 3

z = `5 +- 1/3 (6)`

∴ z = 7 or z = 3

∴ B ≡ (0, 5, 7) or B ≡ (8, –3, 3)

Concept: Scalar Product of Vectors (Dot)

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