Home
Class 12
MATHS
If A B C D is a rhombus whose diagonals ...

If `A B C D` is a rhombus whose diagonals cut at the origin `O ,` then proved that ` vec O A+ vec O B+ vec O C+ vec O D+ vec Odot`

Text Solution

Verified by Experts

Since the diagonals of a rhombus bisect each other, `vec(OA) = - vec(OC) and vec(OB) = - vec(OD)` and so
`vec(OA) + vec(OB) + vec(OC) + vec(OD) = vec0`.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise 1.2|7 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Subjective)|14 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|222 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise All Questions|529 Videos

Similar Questions

Explore conceptually related problems

Let A B C D be a p[arallelogram whose diagonals intersect at P and let O be the origin. Then prove that vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot

A , B , C , D are any four points, prove that vec A B dot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=0.

If 2 vec A C = 3 vec C B , then prove that 2 vec O A =3 vec C B then prove that 2 vec O A + 3 vec O B =5 vec O C where O is the origin.

If vec a , vec b , vec c ,a n d vec d are four non-coplanar unit vector such that vec d make equal angles with all the three vectors vec a , vec ba n d vec c , then prove that [ vec d vec a vec b]=[ vec d vec c vec b]=[ vec d vec c vec a]dot

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

If O( vec0 ) is the circumcentre and O' the orthocentre of a triangle ABC, then prove that i. vec(OA)+vec(OB)+vec(OC)=vec(OO') ii. vec(O'A)+vec(O'B)+vec(O'C)=2vec(O'O) iii. vec(AO')+vec(O'B)+vec(O'C)=2 vec(AO)=vec(AP) where AP is the diameter through A of the circumcircle.

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

A B C D is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opposite sides. If O is any point and vec O A+ vec O B+ vec O C+ vec O D=x vec O E ,t h e nx is equal to a. 3 b. 9 c. 7 d. 4

CENGAGE-INTRODUCTION TO VECTORS -Exercise 1.1
  1. Find the unit vector in the direction of the vector veca=hati+hatj+2h...

    Text Solution

    |

  2. Find the direction cosines of the vector hati+2hatj+3hatk.

    Text Solution

    |

  3. Find the direction cosines of the vector joining the points A(1, 2,3) ...

    Text Solution

    |

  4. The position vectors of Pa n dQ are 5 hat i+4 hat j+a hat k and - hat ...

    Text Solution

    |

  5. Given three points are A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot Then find ...

    Text Solution

    |

  6. Find a vector of magnitude 5 units and parallel to the resultant of th...

    Text Solution

    |

  7. Show that the points A(1, -2, -8) B (5, 0, -2) and C(11, 3, 7) are col...

    Text Solution

    |

  8. If A B C D is a rhombus whose diagonals cut at the origin O , then ...

    Text Solution

    |

  9. Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , re...

    Text Solution

    |

  10. Let A B C D be a p[arallelogram whose diagonals intersect at P and ...

    Text Solution

    |

  11. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

    Text Solution

    |

  12. If vec A O+ vec O B= vec B O+ vec O C , then A ,Bn a dC are (where O ...

    Text Solution

    |

  13. If the sides of an angle are given by vectors veca=hati-2hatj+2hatk an...

    Text Solution

    |

  14. A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD...

    Text Solution

    |

  15. A B C D is a quadrilateral. E is the point of intersection of th...

    Text Solution

    |

  16. What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ...

    Text Solution

    |

  17. The position vectors of points Aa n dB w.r.t. the origin are vec a...

    Text Solution

    |

  18. If vec r1, vec r2, vec r3 are the position vectors off thee collinear...

    Text Solution

    |

  19. If veca and vecb are two vectors of magnitude 1 inclined at 120^(@), t...

    Text Solution

    |

  20. Find the vector of magnitude 3, bisecting the angle between the vector...

    Text Solution

    |