Home
Class 12
MATHS
A1,A2,..., An are the vertices of a regu...

`A_1,A_2,..., A_n` are the vertices of a regular plane polygon with n sides and O as its centre. Show that `sum_(i=1)^(n-1) vec (OA)_i xx vec(OA)_(i+1)=(1-n)(vec (OA)_2 xx vec(OA)_1)`

Promotional Banner

Topper's Solved these Questions

  • Product of two Vectors

    A DAS GUPTA|Exercise Exercise|48 Videos

  • Product of three or more Vectors

    A DAS GUPTA|Exercise Exercise|28 Videos

  • Progression, Related Inequalities and Series

    A DAS GUPTA|Exercise Exercise|235 Videos

Similar Questions

Explore conceptually related problems

A_(1),A_(2),...,A_(n) are the vertices of a regular plane polygon with n sides and O as its centre. Show that sum_(i=1)^(n)vec OA_(i)xxvec OA_(i+1)=(1-n)(vec OA_(2)xxvec OA_(1))

Suppose A_(1), A_(2), …, A_(5) are vertices of a regular pentagon with O as centre. If sum_(i=1)^(4)(OA_(i) times OA_(i+1))=lambda(OA_(1) times OA_(2)) then lambda= _______

Let O be the centre of the regular hexagon ABCDEF then find vec(OA)+vec(OB)+vec(OD)+vec(OC)+vec(OE)+vec(OF)

ABCD is a quadrilateral and E is the point of intersection of the lines joining the middle points of opposite side. Show that the resultant of vec (OA) , vec(OB) , vec(OC) and vec(OD) = 4 vec(OE) , where O is any point.

Given a regular hexagon ABCDEF with centre o,show that vec OB-vec OA=vec OC-vec OD

If A_1A_2....A_n is a regular polygon. Then the vector vec(A_1A_2)+vec(A_2A_3)+.....vec(A_nA_1) is

Let O be the centre of a regular pentagon ABCDE and vec(OA) = veca , then vec(AB) +vec(2BC) + vec(3CD) + vec(4DE) + vec(5EA) is equals:

Let O be the centre of a regular pentagon ABCDE and vec(OA) = veca , then vec(AB) +vec(2BC) + vec(3CD) + vec(4DE) + vec(5EA) is equals:

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

A DAS GUPTA-Product of two Vectors-Exercise
  1. A1,A2,..., An are the vertices of a regular plane polygon with n sides...

    Text Solution

    |

  2. For any vector vec r , prove that vec r=( vec rdot hat i) hat i+( ve...

    Text Solution

    |

  3. If |vec(a)+vec(b)||=|vec(a)-vec(b)| then show that vec(a) and vec(b) a...

    Text Solution

    |

  4. Let hat(a), hat(b) be two unit vectors and theta be the angle between...

    Text Solution

    |

  5. Prove that |vec a + vec b| = sqrt (|vec a|^2 + |vec b|^2 + 2 vec a * ...

    Text Solution

    |

  6. Prove that , ( vec(a) xx vec(b))^(2) + (vec (a).vec(b))^(2) = |ve...

    Text Solution

    |

  7. If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd then show that veca...

    Text Solution

    |

  8. Find the angle between the vectors vec a = 2 vec p + 4 vec q and vec b...

    Text Solution

    |

  9. If |vec a|=1=|vec b| and |vec a + vec b|=sqrt3 then evaluate (2 vec a ...

    Text Solution

    |

  10. Find lambda such that the scalar product of the vector vec i + vec j +...

    Text Solution

    |

  11. The set of values of x for which the angle between the vectors vec a= ...

    Text Solution

    |

  12. Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. ...

    Text Solution

    |

  13. Vectors 3 vec a-5 vec ba n d2 vec a= vec b are mutually perpendicular....

    Text Solution

    |

  14. The pth, qth and rth terms of a GP are the positive numbers a,b and c ...

    Text Solution

    |

  15. If vec a, vec b , vec c are mutually perpendicular vectors of equal ma...

    Text Solution

    |

  16. A line makes angles alpha,beta,gammaa n ddelta with the diagonals of a...

    Text Solution

    |

  17. vec a , vec b and vec c are the position vectors of points A ,B and C...

    Text Solution

    |

  18. Given the vectors vec A , vec B ,a n d vec C form a triangle such tha...

    Text Solution

    |

  19. If AC and BD are the diagonals of a quadrilateral ABCD, prove that its...

    Text Solution

    |

  20. A , B , Ca n dD are any four points in the space, then prove that |...

    Text Solution

    |

  21. If the angle between the vectors x vec i + vec j - vec k and vec i + x...

    Text Solution

    |