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

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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

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

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 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 , 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

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.

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

Let vec r be a unit vector satisfying vec rxx vec a= vec b ,w h e r e| vec a|=sqrt3a n d| vec b|=sqrt2. Then

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 , then A ,Bn a dC are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these

If vec A O+ vec O B= vec B O+ vec O C , then A ,B and C are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these

The scalars la n dm such that l vec a+m vec b= vec c ,w h e r e vec a , vec ba n d vec c are given vectors, are equal to

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Let a three dimensional vector vec V satisfy the condition, 2 vec ...

    Text Solution

    |

  2. If vec a=3 hat i- hat j-4 hat k , vec b=2 hat i+4 hat j-3 hat k and ...

    Text Solution

    |

  3. Let vec O A= vec a , hat O B=10 vec a+2 vec ba n d vec O C= vec b ,w ...

    Text Solution

    |

  4. If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= ...

    Text Solution

    |

  5. If vec x , vec y are two non-zero and non-collinear vectors satisfy...

    Text Solution

    |

  6. Let vec a=alpha hat i+2 hat j-3 hat k , vec b=alpha hat i+2alpha hat ...

    Text Solution

    |

  7. Let vec a , vec b a n d vec c be three vectors having magnitudes 1...

    Text Solution

    |

  8. Two vectors in space are equal only if they have equal component in ...

    Text Solution

    |

  9. Let vec a= hat i- hat j , vec b= hat j- hat ka n d vec c= hat k- hat ...

    Text Solution

    |

  10. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

    Text Solution

    |

  11. If vec axx( vec bxx vec c) is perpendicular to ( vec axx vec b)xx vec...

    Text Solution

    |

  12. [(vecaxxvecb) (veccxxvecd) (vecexxvecf)]is equal to (a)[vecavecbvec...

    Text Solution

    |

  13. vec ba n d vec c are non-collinear if vec axx( vec bxx vec c)+( vec a...

    Text Solution

    |

  14. If veca and vecb are unit vectors, then angle between veca ...

    Text Solution

    |

  15. If vec a| vec b , then vector vec v in terms of vec aa n d vec b sa...

    Text Solution

    |

  16. If vec a^'= hat i+ hat j , vec b^'= hat i- hat j+2 hat k and vec c^' ...

    Text Solution

    |

  17. If vec a= hat i+ hat j , vec b= hat j+ hat k , vec c= hat k+ hat i , ...

    Text Solution

    |

  18. If unit vectors vec aa n d vec b are inclined at angle 2theta such ...

    Text Solution

    |

  19. Let vec a , vec ba n d vec c be three non-coplanar vectors and v...

    Text Solution

    |

  20. Let vec a=a1 hat i+a2 hat j+a2 hat k , vec b=b1 hat i+a2 hat j+b2 hat...

    Text Solution

    |