Find The equation of the perpendicular drawn from the point P(2,4,-1) to the line 
x+5/1=y+3/4=z-6/-9.Also write down the coordinates of the foot of the perpendicuar from P to the line 

Dear Student,   

Please find below the solution to the asked query :



The equation of the given line is :x+51 = y+34 = z-6-9 = k say    ....1The coordinates of any general point on this line are :k-5, 4k-3, 6-9kLet N be the foot of the  drawn from P2,4,-1 on the line 1.Then coordinates of N are Nk-5, 4k-3, 6-9k.Direction ratios of PN are :a1 = k-5-2 = k-7b1 = 4k-3-4 = 4k-7c1 = 6-9k+1 = -9k+7Now, Direction ratios of given line 1 are : 1,4,-9a2,b2,c2Since, PN  line 1, thena1a2 + b1b2 + c1c2 = 0k-7 + 44k-7-9-9k+7 = 0k-7+16k-28+81k-63 = 098k = 98k = 1So, coordinates of foot of  are N-4, 1,-3.Now, equation of PN is :      x - 2-4-2 = y-41-4 = z--1-3--1x-2-6 = y-4-3 = z+1-2

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