Home
Class 12
MATHS
ABCD  is a quadrilateral and  E  is t...

    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.

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

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 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

Show that the straight lines joining the mid - points of the opposite sides of a quadrilateral bisect each other .

C is the midpoint of the line segment bar(AB) and O is any point outside AB, show that vec(OA)+vec(OB)=2vec(OC) .

If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n dB D respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

ABCDE is a pentagon. Prove that the resultant of force vec A B , vec A E , vec B C , vec D C , vec E D and vec A C ,is 3 vec A C .

G is a point inside the plane of the triangle ABC, if vec(GA)+vec(GB)+vec(GC)=vec(0) , then show that G is the centroid of the triangle ABC.

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

E is the mid point of side OB of triangle OAB . D is a point on AB such that AD : DB = 2 : 1 . If OD and AE intersect at P , then -

The distance of the point A(veca) from the line vec(r)=vec(b)+tvec(c) is equal to -

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. The position vectors of points Aa n dB w.r.t. the origin are vec a=...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. A straight line L cuts the lines A B ,A Ca n dA D of a parallelogram A...

    Text Solution

    |

  5. Find the vector of magnitude 3, bisecting the angle between the vec...

    Text Solution

    |

  6. If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 ...

    Text Solution

    |

  7. If vec r1, vec r2, vec r3 are the position vectors of the collinear ...

    Text Solution

    |

  8. Examine the following vector for linear independence: (1) vec i+ve...

    Text Solution

    |

  9. Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n...

    Text Solution

    |

  10. Let vec a , vec ba n d vec c be three units vectors such that 2 vec a...

    Text Solution

    |

  11. Four non –zero vectors will always be a.  linearly dependent       ...

    Text Solution

    |

  12. A boat moves in still water with a velocity which is k times less t...

    Text Solution

    |

  13. In a triangle P Q R ,Sa n dT are points on Q Ra n dP R , respectively,...

    Text Solution

    |

  14. In a quadrilateral P Q R S , vec P Q= vec a , vec Q R = vec b , vec S ...

    Text Solution

    |

  15. solve the differential equation (1+x^2)dy/dx=x

    Text Solution

    |

  16. If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are...

    Text Solution

    |

  17. The position vector of the points P and Q are 5 hat i+7 hat j-2 hat ...

    Text Solution

    |

  18. Consider the vectors hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat...

    Text Solution

    |

  19. If vec A and vec B are two vectors and k any scalar quantity greater ...

    Text Solution

    |

  20. The vectors x hat i+(x+1) hat j+(x+2) hat k ,(x+3) hat i+(x+4) hat j+(...

    Text Solution

    |