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MHT CET202124 Sep 2021Morning ShiftMathematicsThree Dimensional GeometryActual

The co-ordinates of the perpendicular drawn from the point 2 i - j +5 k to the line r =(11 i -2 j -8 k )+ (10 i -4 j -11 k ) are

Options

  1. A(1,-2,3)
  2. B(1,2,-3)
  3. C(-1,2,3)
  4. D(1,2,3)

Correct answer

D. (1,2,3)

Step-by-step solution

We have r =(11 i -2 j -8 k )+ (10 i -4 j -11 k ) So coordinates of any point on this line are [(10 +11),(-11 -2) , (-11 -8)] Let P (2,-1,5) and let M be foot of perpendicular. d.r. of PM are (10 +9),(-4 -1),(-11 -13) Sibce PM is perpendicular to given line, we write aligned & (10 +9)(10)+(4 -1)(-4)+(-11 -13)(-11)=0 & 100 +90+16 +4+121 +143=0 237=-237 & =-1 & M=-10+11,4-2,11-8) i.e. (1,2,3) aligned

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