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MHT CET202416 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The co-ordinates of the foot of the perpendicular from the point (0,2,3) on the line x+3 5 = y+1 2 = z+4 3 is

Options

  1. A( 48 19 , 23 19 , -13 19 )
  2. B( -48 19 , 23 19 , -13 19 )
  3. C( -48 19 , -23 19 , -13 19 )
  4. D( 48 19 , -23 19 , -13 19 )

Correct answer

A. ( 48 19 , 23 19 , -13 19 )

Step-by-step solution

Let x+3 5 = y+1 2 = z+4 3 = Any point on the line is P (5 -3,2 -1,3 -4) Given point is A (0,2,3) The d.r.s. of AP are 5 -3,2 -3,3 -7 Since the line A P is perpendicular to the given line. array ll & 5(5 -3)+2(2 -3)+3(3 -7)=0 & 38 -42=0 & = 21 19 & P ( 48 19 , 23 19 , -13 19 ) array

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