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The foot of the perpendicular form `(2,4,-1)` to the line `x +5 =(1)/(4) (y+3) = -(1)/(9) (z - 6)` isA. `(-4,1,-3)`B. `(4,-1,-3)`C. `(-4,-1,3)`D. `(-4,-1,3)` |
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Answer» Correct Answer - A Given , `(x +5)/(1) = (y+3)/(4) = (z-6)/(-9) = lambda` Any point on the line `P(lambda - 5, 4lambda - 3, -9lambda + 6)` `therefore` Direction ratio of line PQ are. `(lambda - 5 -2,4lambda,-3-4, - 9lambda + 6+1)` ` = (lambda - 7, 4lambda - 7, - 9lambda + 7)` `therefore ` PQ is perpendicular to the given line `because 1(lambda - 7) + 4(4lambda - 7) - 9(-9lambda + 7) = 0` `rArr lambda - 7 + 16lambda - 28 + 81lambda - 63 = 0` `rArr " "lambda = 1` `because` The coordinate of foot of perpendicular are `(-4,1,-3)` |
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