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BITSAT2010MathematicsThree Dimensional GeometryActual

The perpendicular distance of (P(1,2,3) ) from the line ( x-6 3 = y-7 2 = z-7 -2 ) is

Options

  1. A7
  2. B5
  3. C0
  4. D6

Correct answer

A. 7

Step-by-step solution

The point ( A (6,7,7) ) is on the line. Let the perpendicular from ( P ) meet the line in ( L ). Then ( AP ^2=(6-1)^2+(7-2)^2+(7-3)^2=66 ) Also ( AL = ) projection of AP on line ( aligned & ( actual d.c.'s 3 17 , 2 17 , -2 17 ) & (6-1) 3 17 +(7-2) 2 17 +(7-3) -2 17 & = 17 aligned ) ( ) distance ( d ) of ( P ) from the line is given by ( d ^2= AP ^2- AL ^2=66-17=49 so that d =7 )

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