Home
Class 12
MATHS
G is the centroid of a triangle ABC, sho...

G is the centroid of a triangle ABC, show that : `vec(GA)+vec(GB)+vec(GC)=vec0`.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    MODERN PUBLICATION|Exercise Exercise|500 Videos

  • UNIT TEST-4

    MODERN PUBLICATION|Exercise EXERCISE|13 Videos

Similar Questions

Explore conceptually related problems

If Q is the point of intersection of the medians of a triangle ABC, prove that vec(QA)+vec(QB)+vec(QC)=vec0 .

If A,B and C are the vertices of a triangle with position vectors vec(a) , vec(b) and vec(c ) respectively and G is the centroid of Delta ABC , then vec( GA) + vec( GB ) + vec( GC ) is equal to

If G is the centroid of Delta ABC and G' is the centroid of Delta A' B' C' " then " vec(A A)' + vec(B B)' + vec(C C)' =

If O and H be the circumcentre and orthocentre respectively of triangle ABC, prove that vec OA+ vec OB+ vec OC= vec OH .

If S and O be the circumcentre and orthocentre respectively of triangle ABC, prove that vec SA + vec SB + vec SC= vec SO .

If G be the centroid of a triangle ABC, prove that, AB^2+BC^2+CA^2=3(GA^2+GB^2+GC^2)

D,E,F are the middle points of the sides [BC],[CA],[AB] respectively of a triangle ABC. Show that : the sum of the vectors vec(AD),vec(BE),vec(CF) is zero.

Orthocenter of an equilateral triangle ABC is the origin O. If vec(OA)=veca, vec(OB)=vecb, vec(OC)=vecc , then vec(AB)+2vec(BC)+3vec(CA)=

In pentagon ABCDE, prove that : vec(AB)+vec(BC)+vec(CD)+vec(DE)+vec(EA)=vec0 .

ABCD is a parallelogram and P the intersection of the diagonals, O is any point . Show that vec(OA)+vec(OB)+vec(OC)+vec(OD)=4vec(OP) .

MODERN PUBLICATION-VECTORS-Exercise
  1. If veca,vecb,vecc,vecd respectively, are position vectors representing...

    Text Solution

    |

  2. If Q is the point of intersection of the medians of a triangle ABC, pr...

    Text Solution

    |

  3. G is the centroid of a triangle ABC, show that : vec(GA)+vec(GB)+vec(G...

    Text Solution

    |

  4. Let veca,vecb,vecc,vecd be the position vectors of the four distinct p...

    Text Solution

    |

  5. Show that the line joining any vertex of a parallelogram to the mid-po...

    Text Solution

    |

  6. Prove that the figure formed by joining the mid-points of the pairs of...

    Text Solution

    |

  7. Show that if P,A,B are any three points, then lambda vec(PA)+mu vec(PB...

    Text Solution

    |

  8. Obtain the dot product of the vectors : veca=veci-hatj+hatk and vecb=v...

    Text Solution

    |

  9. Write the magnitude of a vector veca in terms of dot product.

    Text Solution

    |

  10. If veca=7hati+hatj-4hatk and vecb=2hati+6hatj+3hatk find the projectio...

    Text Solution

    |

  11. Let veca=2hati+3hatj+2hatk and vceb=hati+2hatj+hatk. Find the projecti...

    Text Solution

    |

  12. Find the projection of the vector hati-hatj on the vector hati+hatj.

    Text Solution

    |

  13. Find veca.vecb If veca=3hati-hatj+2hatk and vecb=2hati+3hatj+3hatk

    Text Solution

    |

  14. Find veca.vecb If veca=2hati-hatj+hatk and vecb=2hatj-hatk.

    Text Solution

    |

  15. Evaluate the product (3 hata-5hatb) cdot(2hata+7hatb)

    Text Solution

    |

  16. If veca is a unit vector and (vecx - veca) cdot (vecx + veca) = 8, th...

    Text Solution

    |

  17. If veca is a unit vcetor and (vecx-veca)*(vecx+veca)=80, then find |ve...

    Text Solution

    |

  18. If vecp is a unit vcetor and (vecx-vecp)*(vecx+vecp)=80, then find |ve...

    Text Solution

    |

  19. Find |vecx|, if for a unit vector veca, (vecx - veca)cdot(vecx+veca)...

    Text Solution

    |

  20. Find the angle between the vectors : hati-hatj and hatj-hatk.

    Text Solution

    |