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MHT CET202526 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

A triangle ABC is formed by A (1,-1,0), B (3,5,3), C (-11,-5,6) . The equation of internal angle bisector of angle A is

Options

  1. A(1-x) 2 = y-(-1) 2 = z 3
  2. Bx+1 2 = y-1 2 = z 3
  3. Cx+2 1 = y-2 1 = z 3
  4. Dx-2 1 = y+3 2 = z 3

Correct answer

A. (1-x) 2 = y-(-1) 2 = z 3

Step-by-step solution

Given triangle vertices A(1, -1, 0) , B(3, 5, 3) , and C(-11, -5, 6) , the position vectors from A are: AB = (2, 6, 3) , with magnitude 7 AC = (-12, -4, 6) , with magnitude 14 The unit vectors are u _ AB = ( 2 7 , 6 7 , 3 7 ) and u _ AC = (- 6 7 , - 2 7 , 3 7 ) . The direction vector of the angle bisector is given by their sum: d = u _ AB + u _ AC = (- 4 7 , 4 7 , 6 7 ) Multiplying by 7 yields the proportional vector (-4, 4, 6) , which simplifies to (-2, 2, 3) when divided by 2 . The bisector line passes through A(

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