Home
Class 12
MATHS
In pentagon ABCDE, prove that : vec(AB)+...

In pentagon ABCDE, prove that : `vec(AB)+vec(BC)+vec(CD)+vec(DE)+vec(EA)=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 A,B,C and D are any four points in space prove that |quad vec (AB) xx vec (CD)+ vec (BC) xx vec (AD) + vec (CA) xx vec (BD)|=4(area of Delta ABC) .

ABCDEF is a regular hexagon. Express the vectors vec (CD) , vec (DE) , vec (EF) , vec (FA) , vec (CE) in terms of vec (AB) and vec (BC) .

ABCD is a parallelogram and AC, BD are its diagonals. Show that : vec(AC)+vec(BD)=2vec(BC),vec(AC)-vec(BD)=2vec(AB) .

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

ABCDE is a pentagon. Prove that the resultant of forces vec (AB), vec(AE), vec(BC), vec(DC), vec(ED) and vec(AC) is 3vec(AC) .

Statement 1 : In DeltaABC , vec(AB) + vec(BC) + vec(CA) = 0 Statement 2 : If vec(OA) = veca, vec(OB) = vecb , then vec(AB) = veca + vecb

If ABCDEF is a regular hexagon with vec(AB) = vec(a) ,vec(BC ) = vec(b) then vec(CE) equals :

Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

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) .

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

MODERN PUBLICATION-VECTORS-Exercise
  1. Give a condition that the three vectors veca,vecb and vecc form the th...

    Text Solution

    |

  2. D,E,F are mid-points of the sides of the triangle ABC, show that for a...

    Text Solution

    |

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

    Text Solution

    |

  4. ABCD is a parallelogram and AC, BD are its diagonals. Show that : vec(...

    Text Solution

    |

  5. ABCDEF is a regular hexagon. Show that : vec(OA)+vec(OB)+vec(OC)+vec(O...

    Text Solution

    |

  6. If ABCDEF is a regular hexagon and AB+AC+AD+AE+AF=lamdaAD, then lamda ...

    Text Solution

    |

  7. ABCDEF is a regular hexagon. Show that : vec(AB)+vec(AC)+vec(AD)+vec(A...

    Text Solution

    |

  8. Prove that |veca|-|vecb| le|veca - vecb |.

    Text Solution

    |

  9. If veca+5vecb=vecc and veca -7 vecb =2vecc, then show that veca has th...

    Text Solution

    |

  10. Write two different vectors having same magnitude.

    Text Solution

    |

  11. Write two different vectors having same direction.

    Text Solution

    |

  12. Find the sum of the vectors veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5ha...

    Text Solution

    |

  13. Find the vector with initial point P(-4,2) and terminal point Q(0,-4).

    Text Solution

    |

  14. Find a unit vector in the direction from : P(3,2) towards Q(5,6).

    Text Solution

    |

  15. Find a unit vector in the direction from : P(1,2) towards Q(4,5).

    Text Solution

    |

  16. Compute the magnitude of the following vectors: vecc=(1/sqrt3)veci+(1/...

    Text Solution

    |

  17. Find the magnitude of the vector hati-3hatj+4hatk.

    Text Solution

    |

  18. Find the value of x for which x(hati + hatj + hatk) is a unit vector.

    Text Solution

    |

  19. Find the unit vector in the direction of the vector veca=hati+hatj+2ha...

    Text Solution

    |

  20. Find the unit vector in the direction of the vector : veca =2hati+3hat...

    Text Solution

    |