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MHT CET202313 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The incentre of the triangle ABC , whose vertices are A (0,2,1), B (-2,0,0) and C (-2,0,2) , is

Options

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

Correct answer

A. (- 3 2 , 1 2 , 1 )

Step-by-step solution

Let a =2 j + k , b =-2 i , c =-2 i +2 k AB =-2 i -2 j - k , BC =2 k aligned & AC =-2 i -2 j + k & | AB |=3,| BC |=2,| AC |=3 aligned Incentre of ABC is given by | AB | c +| BC | a +| AC | b | AB |+| BC |+| AC | aligned & = 3(-2 i +2 k )+2(2 j + k )+3(-2 i ) 3+2+3 & = -12 i +4 j +8 k 8 & =- 3 2 i + 1 2 j + k aligned

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