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MHT CET20242 May 2024Evening ShiftMathematicsStraight LinesActual

The incentre of the triangle whose vertices are P (0,3,0), Q (0,0,4) and R (0,3,4) is

Options

  1. A(0,3,2)
  2. B(0,2,3)
  3. C(2,0,3)
  4. D(2,3,0)

Correct answer

B. (0,2,3)

Step-by-step solution

array ll & Let p =3 j , q =4 k , r =3 j +4 k & PQ =-3 j +4 k & QR =3 j & PR =4 k & | PQ |=5,| QR |=3,| PR |=4 array Incentre of PQR is given by aligned & | PQ | r +| QR | p +| PR | q | PQ |+| QR |+| PR | & = 5(3 j +4 k )+3(3 j )+4(4 k ) 5+3+4 & = 24 j +36 k 12 & =2 j +3 k & Incentre (0,2,3) aligned

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