Home
Class 12
MATHS
ABCD is a quadrilateral and E is the poi...

ABCD is a quadrilateral and E is the point of intersection of the lines joining the mid-points of opposite sides. If O be any point in the plane, then show that `vec(OA)+vec(OB)+vec(OC)+vec(OD)=4vec(OE)`.

A

`3`

B

`4`

C

`7`

D

`9`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    NIKITA PUBLICATION|Exercise MCQs|404 Videos

Similar Questions

Explore conceptually related problems

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.

ABCD is a quadrilateral. E is the point of intersection of the line joining the mid-points of the oppsote sides. If O is any point and OA+OB+OC+OD=xOE, then x is equal to

ABCD is a quadrilateral and G the point of intersection of the lines joining the middle points of opposite sides .IF o is any point prove that bar(OA)+bar(OB)+bar(OC)+bar(OD)=bar(4OG)

ABCD 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 OA+vec OB+vec OC+vec OD=xvec OE, then x is equal to a.3 b.9 c.7 d.4

ABCD are four points in a plane and Q is the point of intersection of the lines joining the mid-points of AB and CD;BC and AD. Show that vec PA+vec PB+vec PC+vec PD=4vec PQ where P is any point.

ABCDEF is a regular hexagon. Show that : vec(OA)+vec(OB)+vec(OC)+vec(OD)+vec(OE)+vec(OF)=vec(0)

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

If D E and F be the mid ponts of the sides BC, CA and AB respectively of the /_\ABC and O be any point, then prove that vec(OA)+vec(OB)+vec(OC)=vec(OD)+vec(OE)+vec(OF)

ABCD is a quadrilateral and O is point in its plabe such that vec OA+vec OB+vec OC+vec OD=0 show that 0 is the pooint of intersection of the lines joining the mid points of the opposite sides of quadrilateral ABCD.

ABCD is parallelogram and P is the point of intersection of its diagonals.If O is the origin of reference,show that vec OA+vec OB+vec OC+vec OD=4vec OP

NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
  1. In the quadrilateral ABCD :

    Text Solution

    |

  2. Let square PQRS be a quadrilateral. If M and N are the mid-points of t...

    Text Solution

    |

  3. ABCD is a quadrilateral and E is the point of intersection of the line...

    Text Solution

    |

  4. If hat(i)+hat(j)-hat(k), 2hat(i)+3hat(j), 3hat(i)+5hat(j)-2hat(k) and ...

    Text Solution

    |

  5. E and F are mid-points of sides of AD and BC respectively of quadrila...

    Text Solution

    |

  6. Which of the following is trues?

    Text Solution

    |

  7. OABC is a tetrahedron D and E are the mid points of the edges vec (OA)...

    Text Solution

    |

  8. If M and N are the mid-points of the diagonals AC and BD respectively ...

    Text Solution

    |

  9. ABCD is a rhombus and P, Q, R and S are wthe mid-points of the side...

    Text Solution

    |

  10. If P, Q are the mid-points of the diagonals AC and BD of a quadrilater...

    Text Solution

    |

  11. If ABCD is a quadrilateral, then 2overline(AB)+3overline(BC)+2overline...

    Text Solution

    |

  12. If ABCD is a square, then bar(AB) + 2 bar(BC) + 3 bar(CD) + 4 bar(DA...

    Text Solution

    |

  13. ABCD is a parallelogram with AC and BD as diagonals. Then, A vec C - ...

    Text Solution

    |

  14. Let ABCD is a parallelogram and vecAC, vecBD be its diagonal, then vec...

    Text Solution

    |

  15. ABDC is a parallelogram and P is the point of intersection of its diag...

    Text Solution

    |

  16. ABCD is a parallelogram and O is the point of intersection of its diag...

    Text Solution

    |

  17. In parallelogram ABCD,if P, Q are mid-points of BC and CD respectively...

    Text Solution

    |

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

    Text Solution

    |

  19. If PQRST is a pentagon, then overline(PQ)+overline(PR)+overline(PS)-ov...

    Text Solution

    |

  20. ABCDE is a pentagon. The resultant of the vectors overline(AB), overli...

    Text Solution

    |