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MHT CET2012MathematicsVector Algebra

If in a A B C, O and O ^ are the incentre and orthocentre respectively, then ( O ^ A + O ^ B . .+ O ^ C ) is equal to

Options

  1. A2 O ^ O
  2. B0^ 0
  3. C00^
  4. D2 OO

Correct answer

A. 2 O ^ O

Step-by-step solution

O' A = O ^ O + O A O ^ B = O ^ O + O B O ^ C = O ^ O + O C O ^ A + O ^ B + O ^ C =3 0 0 +( O A + O B + O C ) ( i ) O A + O B + O C = O O ^ =- O ^ O O ^ A + O ^ B + O ^ C =3 O ^ O - O ^ O [from Eq. (i)] O ^ A + O ^ B + O ^ C =2 O ^ O

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