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MHT CET202121 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The direction cosines , m , n of the line x +2 2 = 2 y -4 3 ; z =-1

Options

  1. A= 1 5 , ~m =0,= 2 5
  2. B= 3 5 , ~m = 4 5 , n =0
  3. C= 4 5 , ~m = 3 5 , n =0
  4. D= 1 3 , ~m = 1 3 , n = 1 3

Correct answer

C. = 4 5 , ~m = 3 5 , n =0

Step-by-step solution

We have line x+2 2 = 2 y-5 3 , z=-1 i.e. x-(-2) 2 = 2 (y- 5 2 ) 3 , z=-1 i.e. x-(-2) 2 = (y- 5 2 ) ( 3 2 ) , z=-1 Here direction ratios are 2, 3 2 Also (2)^2+ ( 3 2 )^2+0 = 5 2 Here required direction cosines are 2 ( 5 2 ) , ( 3 2 ) ( 5 2 ) , 0 ( 5 2 ) i.e. 4 5 , 3 5 , 0

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