Home
Class 12
MATHS
If O\ a n d\ O^(prime) are circumcentre ...

If `O\ a n d\ O^(prime)` are circumcentre and orthocentre of `\ A B C ,\ t h e n\ vec O A+ vec O B+ vec O C` equals `2 vec O O '` b. ` vec O O '` c. ` vec O ' O` d. `2 vec O ' O`

A

`2O' O `

B

`O'O `

C

`OO' `

D

`2OO' `

Text Solution

Verified by Experts

The correct Answer is:
A
O'A = O'O + OA
O'C = O'O +OC

`rArr O'A + O'B + O'C `
` = 3O'O + (OA + OB + OC) `… (i)
` because OA + OB + OC = OO' =-O'O `
` therefore O'A + O'B +O'C = 3O'O -O'O ` [From Eq. (i) ]
O'A + O'B + O'C= 2O'O
Promotional Banner

Topper's Solved these Questions

  • MHTCET 2011

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise METHEMATICS|50 Videos

  • MHTCET 2016

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Mathematics|50 Videos

Similar Questions

Explore conceptually related problems

If O\ a n d\ O^(prime) are circumcentre and orthocentre of \ A B C ,\ t h e n\ vec O A+ vec O B+ vec O C equals a. 2 vec O O ' b. vec O O ' c. vec O ' O d. 2 vec O ' O

If S is circumcentre, O is orthocentre of DeltaABC , then vec(SA)+vec(SB)+vec(SC) =

If O is the circumcentre and P the orthocentre ( of Delta ABC, prove that )/(OA)+vec OB+vec OC=vec OP

If O is the circumcentre,G is the centroid and O' is orthocentre or triangle ABC then prove that: vec OA+vec OB+vec OC=vec OO

If S is the cirucmcentre, G the centroid, O the orthocentre of a triangle ABC, then vec(SA) + vec(SB) + vec(SC) is:

Let O be an interior point of Delta ABC such that 2vec OA+5vec OB+10vec OC=vec 0

If vec a + vec b + vec c = o, prove that vec a xxvec b = vec b xxvec c = vec c xxvec a

If G denotes the centroid of Delta ABC, then write the value o vec GA+vec GB+vec GC

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MHTCET 2012-MATHEMATICS
  1. The value of int0^oox/((1+x)(x^2+1))dx is

    Text Solution

    |

  2. The area of the region bounded by the curves y^(2)=8x and y = x (in sq...

    Text Solution

    |

  3. If O\ a n d\ O^(prime) are circumcentre and orthocentre of \ A B C ,\ ...

    Text Solution

    |

  4. If veca+vecb+vecc=vec0, |veca| = 3, |vecb| = 5, |vecc| = 7, then angle...

    Text Solution

    |

  5. i(jxx k ) + j ( k xx i) + k (j xx i) is equal to

    Text Solution

    |

  6. One card is drawn at random from a pack of playing cards the p...

    Text Solution

    |

  7. 15 coins are tossed , the probability of getting heads will be

    Text Solution

    |

  8. The odds against solving a problem by A and B are 3 :2 and 2 : ...

    Text Solution

    |

  9. The line lx+my+n=0 is a normal to the parabola y^2 = 4ax if

    Text Solution

    |

  10. The line 2x+y+lamda=0 is a normal to the parabola y^(2)=-8x, is lamda=

    Text Solution

    |

  11. The line lx+my+n=0 is a normal to the parabola y^2 = 4ax if

    Text Solution

    |

  12. f : Rto R, then f ( x ) = x |x| will be

    Text Solution

    |

  13. lim ( x to pi//2 ) ( sec x - tan x ) is equal to

    Text Solution

    |

  14. If f(x)={((log(1+2ax)-log(1-bx))/(x)",", x ne 0),(k",", x =0):} is con...

    Text Solution

    |

  15. If f ( x ) = |x - 3|, then f' ( 3 ) is

    Text Solution

    |

  16. If tan x = (2t)/(1 -t^(2)) " and sin y" = (2t)/(1 + t^(2)) , then the...

    Text Solution

    |

  17. If x^(p) + y^(q) = (x + y)^(p+q) , " then" (dy)/(dx) is

    Text Solution

    |

  18. All points on the curve y^(2)=4a(x+a" sin"(x)/(a)) at which the tangen...

    Text Solution

    |

  19. The length of normal at any point to the curve, y=c cosh(x/c) is

    Text Solution

    |

  20. The height of right circular cylinder of maximum volume in a sphere of...

    Text Solution

    |