Home
Class 12
MATHS
Let vec(OA) =veca, vec(OB) = 10veca + 2v...

Let `vec(OA) =veca, vec(OB) = 10veca + 2vecb and vec(OC) =vecb` where , O, A and C are non-collinear points. Let p denote that area of the quadrilateral OABC. And let q denote the area of the parallelogram with OA and OC as adjacent sides. If p=kq, then k= _________

Text Solution

Verified by Experts

The correct Answer is:
6
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE) (INTEGER TYPE)|4 Videos
  • VECTORS

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

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE)|60 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

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

ABCD is a quadrilateral with vec(AB) = veca, vec(AD) = vecb and vec(AC)=2veca+3vecb. If its area is alpha times the area of the parallelogram with AB and AD as adjacent sides, then alpha=

If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd , where veca, vecb are non-collinear and vec c, vec d are also non-collinear then :

Let vec(OA)=hati+3hatj-2hatk and vec(OB)=3hati+hatj-2hatk. Then vector vec(OC) biecting the angle AOB and C being a point on the line AB is

If veca,vecb,vec c are position vectors of the non- collinear points A, B, C respectively, the shortest distance of A from BC is

The adjacent sides of a parallelogram are vec(P)=2i-3j+k and vec(Q)=-2i+4j-k . What is the area of the parallelogram ?

Let veca , vecb , vecc represent respectively vec(BC), vec(CA) and vec(AB) where ABC is a triangle , Then ,

If vec a , vec ba n d vec c are any three non-coplanar vectors, then prove that points are collinear: veca+ vecb+vecc , 4veca+3vecb ,10veca+7vec b-2vecc .

VMC MODULES ENGLISH-VECTORS -JEE ADVANCED (ARCHIVE)
  1. Let PQR be a triangle . Let veca=overline(QR),vecb = overline(RP) and ...

    Text Solution

    |

  2. Let O be the origin and let PQR be an arbitrary triangle. The point S ...

    Text Solution

    |

  3. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

    Text Solution

    |

  4. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

    Text Solution

    |

  5. The components of a vector veca along and perpendicular to a non-zero ...

    Text Solution

    |

  6. A, B C and D are four points in a plane with position vectors, veca, v...

    Text Solution

    |

  7. Let vecA , vecB and vecC be vectors of legth , 3,4and 5 respectively. ...

    Text Solution

    |

  8. If vecb and vecc are any two mutually perpendicular unit vectors and v...

    Text Solution

    |

  9. Find a unit vector pependicular to the plane determined by the points ...

    Text Solution

    |

  10. the area of the triangle whose vertices are A ( 1,-1,2) , B ( 1,2, -1)...

    Text Solution

    |

  11. Let vec(OA) =veca, vec(OB) = 10veca + 2vecb and vec(OC) =vecb where , ...

    Text Solution

    |

  12. If the vectors ahati+hatj+hatk, hati+bhatj+hatk, hati+hatj+chatk(a!=1,...

    Text Solution

    |

  13. If vecA,vecB,vecC are non-coplanar vectors than ( vecA . vecB xx vecC...

    Text Solution

    |

  14. If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3)|=0 and vectors (1,a,a^2)...

    Text Solution

    |

  15. let veca , vecb and vecc be three vectors having magnitudes 1, 1 and 2...

    Text Solution

    |

  16. A non vector veca is parallel to the line of intersection of the plane...

    Text Solution

    |

  17. The vector(s) which is /are coplanar with vectors hati +hatj + 2hatk a...

    Text Solution

    |

  18. Let vecb= 4 hati + 3hatj and vecc be two vectors perpendicular to each...

    Text Solution

    |

  19. If vecA = ( 1,1,1) and vecC= (0, 1,-1) are given vectors the vector ve...

    Text Solution

    |

  20. Consider the cube in the first octant with sides OP,OQ and OR of lengt...

    Text Solution

    |