Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Sum

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

Advertisement Remove all ads

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)
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×