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Manipal MET2022MathematicsThree Dimensional Geometry

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

Correct answer

10.893

Step-by-step solution

It is given that point Q ( 5 3 , 7 3 , 15 4 ) is foot of perpendicular of point P(0,2,1) to a line passes through point A( , 5,1) . So, P Q A Q . Direction ratios of line segments P Q is ( 5 3 , 1 3 , 11 4 ) and direction ratios of line A Q is ( - 5 3 , 8 3 ,- 11 4 ) . array cc & 5 3 ( - 5 3 )+ 1 3 8 3 + 11 4 (- 11 4 )=0 & 15 -25+8+ 99(-11) 16 =0 & 15 -17= 99 11 16 & 5 = 1089-817 16 & 5 =54.466 =10.893 array

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