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MHT CET202526 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

The direction cosines of a normal to the plane passing throgh (4,2,3) , (-1,4,2) and (3,2,1) are .....

Options

  1. A-2 101 , 3 101 , 8 101
  2. B-3 49 , 2 49 , 6 49
  3. C-4 101 , -9 101 , 2 101
  4. D4 22 , -12 22 , 18 22

Correct answer

C. -4 101 , -9 101 , 2 101

Step-by-step solution

Given points A(4,2,3) , B(-1,4,2) , and C(3,2,1) , vectors in the plane are identified as AB = (-5,2,-1) and AC = (-1,0,-2) . The normal vector n is determined by the cross product n = AB AC : n = (-4, -9, 2) Direction cosines are obtained by dividing each component by the magnitude | n | = 101 , yielding ( -4 101 , -9 101 , 2 101 ) , which corresponds to option C .

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