If O be the circumcentre and O' be the orthocentre of the `DeltaABC`, then `O'A+O'B+O'C` is equal to

Options

A. Statement - 1 is True, Statement - 2 is True , Statement - 2 is a correct explanation for Statement - 1.
B. Statement -1 is True, Statement - 2 is True, Statement -2 is not a correct explanation for Statement - 1.
C. Statement - 1 is True, Statement - 2 is False.
D. Statement - 1 is False, Statement - 2 is True.

Answer

A

Explanation

Clearly, statement -2 is true .
Replacing S by O' in statement -2, we get
` vec(O'A) + vec(O'B) + vec(O'C) = 3 vec(O'G)`
`rArr vec(O'A) + vec(O'B) + vec(O'C) = 2 vec(O'G)+vec(O'G)`
`rArr vec(O'A) + vec(O'B) + vec(O'C) = 2vec(O'G)+2 vec(GO) " "[because 2 OG = GO']`
`rArr vec(O'A) + vec(O'B) + vec(O'C) = 2( vec(O'G)+vec(GO))`
`rArr vec(O'A) + vec(O'B) + vec(O'C) = 2 vec(O'O)`