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Manipal MET2023MathematicsThree Dimensional Geometry

If the foot of the perpendicular drawn from the point (2,0,1) on a line passing through ( , 5,1) is ( 7 3 , 5 3 , 15 4 ) , then is equal to_____

Correct answer

4.372

Step-by-step solution

It is given that Q ( 7 3 , 5 3 , 15 4 ) is foot of perpendicular of point P(2,0,1) to a line passes through point A( , 5,1) . So P Q A Q Direction ratios of line segments P Q is ( 7 3 , 5 3 , 15 4 ) and direction ratios of line A Q is ( - 7 3 , 10 3 ,- 11 4 ) Since, P Q and A Q is perpendicular to each other, so P Q A Q=0 7 3 ( - 7 3 )+ 5 3 10 3 + 15 4 (- 11 4 )=0 7(3 -7) 9 + 50 9 - 165 16 =0 aligned & 336 -784+800-1485 144 =0 & 336 =1469 = 1469 336 =4.372 aligned

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