Home
Class 12
MATHS
Let vec O A= vec a , vec O B=10 vec a+2...

Let ` vec O A= vec a , vec O B=10 vec a+2 vec b ,a n d vec O C=bw h e r eO` is origin. Let `p` denote the area of th quadrilateral `O A B Ca n dq` denote the area of teh parallelogram with `O Aa n dO C` as adjacent sides. Prove that `p=6qdot`

A

6

B

2

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    VMC MODULES ENGLISH|Exercise LEVEL -2|47 Videos

  • VECTORS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos

  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE) (TRUE/ FALSE)|30 Videos

  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

Let vec O A= vec a , vec O B=10 vec a+2 vec ba n d vec O C= vec b ,w h e r eO ,Aa n dC are non-collinear points. Let p denotes the areaof quadrilateral O A C B , and let q denote the area of parallelogram with O Aa n dO C as adjacent sides. If p=k q , then find kdot

Let vec O A= vec a , hat O B=10 vec a+2 vec ba n d vec O C= vec b ,w h e r eO ,Aa n dC are non-collinear points. Let p denotes the areaof quadrilateral O A C B , and let q denote the area of parallelogram with O Aa n dO C as adjacent sides. If p=k q , then find kdot

if vec Ao + vec O B = vec B O + vec O C ,than prove that B is the midpoint of AC.

If vec A O+ vec O B= vec B O+ vec O C , prove that A , B , C are collinear points.

If vec A O+ vec O B= vec B O+ vec O C , prove that A , B , C are collinear points.

A B C D is quadrilateral such that vec A B= vec b , vec A D= vec d , vec A C=m vec b+p vec ddot Show that he area of the quadrilateral A B C Di s1/2|m+p|| vec bxx vec d|dot

If vec P O+ vec O Q= vec Q O+ vec O R , show that the point, P ,Q ,R are collinear.

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec c- vec a , then show that A B C D is parallelogram.

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec a- vec d , then show that A B C D is parallelogram.

if vec (AO) + vec (O B) = vec (B O) + vec (O C) ,than prove that B is the midpoint of AC .

VMC MODULES ENGLISH-VECTORS -LEVEL -1
  1. The length of the longer diagonal of the parallelogram constructed on ...

    Text Solution

    |

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

    Text Solution

    |

  3. Let vec O A= vec a , vec O B=10 vec a+2 vec b ,a n d vec O C=bw h e r...

    Text Solution

    |

  4. ABCDEF is a regular hexagon with centre a the origin such that vec(AB)...

    Text Solution

    |

  5. ABCD a parallelogram, and A1 and B1 are the midpoints of sides BC and ...

    Text Solution

    |

  6. The vertices of a triangle have the position vectors veca,vecb,vecc an...

    Text Solution

    |

  7. If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc...

    Text Solution

    |

  8. Vectors veca,vecb and vecc are of the same length and when taken pair-...

    Text Solution

    |

  9. If three vectors veca, vecb,vecc are such that veca ne 0 and veca xx v...

    Text Solution

    |

  10. veca,vecb,vecc are three non-coplanar vectors such that veca+vecb+vecc...

    Text Solution

    |

  11. If S is the cirucmcentre, G the centroid, O the orthocentre of a trian...

    Text Solution

    |

  12. If veca, vecb, vecc are three non-zero vectors such that veca + vecb +...

    Text Solution

    |

  13. Let alpha,beta and gamma be distinct real numbers. The points with pos...

    Text Solution

    |

  14. If |veca|=4, |vecb|=4 and |vecc|=5 such that veca bot vecb + vecc, vec...

    Text Solution

    |

  15. If vecu=veca-vecb, vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvec...

    Text Solution

    |

  16. If the vectors vecc, \ veca=xhati+yhatj+zhatk and vecb=hatj are such ...

    Text Solution

    |

  17. Given any vector, vecr,|vecr xx hati|^(2) + |vecr xx hatj|^(2) + |vecr...

    Text Solution

    |

  18. The value of x fot which the angle between the vectors a=-3hat(i)+xhat...

    Text Solution

    |

  19. If a,b and c are non-coplanar vectors and lamda is a real number, then...

    Text Solution

    |

  20. Let vecb and vecc be non-collinear vectors. If veca is a vector such t...

    Text Solution

    |