InterviewSolution
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InterviewSolution
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Find the equation of the perpendicular drawn from (2,4,-1) to the line `(x+5)/1=(y+3)/4=(z-6)/3`.A. ` ( x - 2 ) / ( 6 ) = ( y - 4 ) /( 3 ) = ( z+ 1 ) / ( 2 ) `B. ` ( x + 2 ) / ( 6 ) = ( y - 4 ) /( 3 ) = ( z + 1 ) /( 2 ) `C. ` ( x + 2 ) /( - 6 ) = ( y - 4 ) / ( 3) = ( z + 1 ) / ( 2 ) `D. ` ( x + 2 ) /( 6 ) = ( y + 4 ) / ( 3) = ( z+ 1 ) / ( 2 ) ` |
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Answer» Correct Answer - A Given equation of line in ` ( x + 5 ) / ( 1 ) = ( y+ 3 ) / ( 4 ) = ( z- 6 ) /( - 9 ) = lamda ` [say] Any point on the line is ` ( lamda - 5, 4lamda - 3, - 9 lamda + 6 ) ` Now, directions ratio of PQ are ` ( lamda - 5 - 2, 4lamda - 3 - 4, - 9 lamda + 6 + 1 ) ` i.e, ` ( lamda - 7, 4lamda - 7, 9lamda + 7 ) ` Since, PQ is perpendicular to the given line, ` therefore 1 ( lamda - 5) + 4 ( 4lamda - 7 ) - 9 ( - 9 lamda + 7 ) = 0 ` ` " "[ because a_ 1 a _ 2 + b _ 1 b _ 2 + c _ 1 c_ 2 = 0 ] ` ` rArr 9 lamda - 96 = 0 rArr lamda = 1 ` ` therefore ` Foot of perpendicular ` Q ( 1 - 5, 4 - 3 , - 9 + 6 ) ` i.e, `Q ( - 4, 1, - 3 ) ` The equation of the line passing through ` P ( 2, 4 , -1 ) and N ( -4, 1, - 3 ) ` is ` ( x - 2 ) / ( 6 ) = ( y - 4 ) /( 3 ) = ( z + 1)/( 2 ) ` or ` ( x - 2 ) / ( 6 ) = ( y - 4 ) / ( 3 ) = ( z + 1 ) / ( 2 ) ` |
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