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