Home
Class 12
MATHS
A parallelogram is constructed on 3 v...

A parallelogram is constructed on `3 vec a+ vec ba n d vec a-4 vec b ,w h e r e| vec a|=6a n d| vec b|=8,a n d vec aa n d vec b` are anti-parallel. Then the length of the longer diagonal is `40` b. `64` c. `32` d. `48`

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

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 vec r =?

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

Statement 1: | vec a|=3,| vec b|= 4 a n d | vec a+ vec b|=5,t h e n| vec a- vec b|=5. Statement 2: The length of the diagonals of a rectangle is the same.

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is parallel to vec b- vec c

If vec axx vec b= vec cxxvec d and vec axxvec c= vec bxxvec d, vec a ne vec d, vec b ne vec c then show that vec b- vec c is parallel to vec a-vec d

If vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=sqrt3\ a n d\ vec adot vec b=1, find the angle between vec a\ a n d\ vec b .

Let vec a , vec ba n d vec c be pairwise mutually perpendicular vectors, such that | vec a|=1,| vec b|=2,| vec c|=2. Then find the length of | vec a+ vec b+ vec c |

Given | vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3). If vec c is a vector such that vec c- vec a-2 vec b=3( vec axx vec b), then find the value of vec c. vec b

Show that | vec a| vec b+| vec b| vec a is a perpendicular to | vec a| vec b-| vec b| vec a , for any two non-zero vectors vec aa n d vec bdot

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. The value of x for which the angle between vec a=2x^2 hat i+4x hat ...

    Text Solution

    |

  2. Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and th...

    Text Solution

    |

  3. A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b...

    Text Solution

    |

  4. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lam...

    Text Solution

    |

  5. If a \ "a n d" \ c are unit vectors and |b|=4 . The angle between a ...

    Text Solution

    |

  6. If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vec...

    Text Solution

    |

  7. If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec ...

    Text Solution

    |

  8. If vec a \ a n d \ vec b are two non-collinear unit vector, and ...

    Text Solution

    |

  9. The angles of triangle, two of whose sides are represented by vector...

    Text Solution

    |

  10. vec a , vec b ,a n d vec c are unimodular and coplanar. A unit vector...

    Text Solution

    |

  11. Vectors perpendicular to hat i- hat j- hat k and in the plane of hat...

    Text Solution

    |

  12. If side vec A B of an equilateral trangle A B C lying in the x-y plan...

    Text Solution

    |

  13. If vec a, vec b,vec c and vec d are unit vectors such that (vec a xx v...

    Text Solution

    |

  14. Let two non-collinear unit vector hat a a n d hat b form an acute a...

    Text Solution

    |

  15. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

    Text Solution

    |

  16. If vec a , vec b and vec c are three non-zero, non coplanar vector...

    Text Solution

    |

  17. The unit vector which is orthogonal to the vector 3 hat i+2 hat j+6 ...

    Text Solution

    |

  18. If vec a and vec b are unequal unit vectors such that ( vec a- vec ...

    Text Solution

    |

  19. If veca,vecb,vecc are 3 unit vectors such that vecaxx(vecbxxvecc)=vec...

    Text Solution

    |

  20. Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, ve...

    Text Solution

    |