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. Column I, Column II The possible value of vec a if vec r=( hat i+ ha...

    Text Solution

    |

  2. If vec A, vec B and vec C are vectors such that |vec B|=|vec C|. Prove...

    Text Solution

    |

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

    Text Solution

    |

  4. Statement 1: Vector vec c=-5 hat i+7 hat j+2 hat k is along the bisec...

    Text Solution

    |

  5. Statement 1: A component of vector vec b=4 hat i+2 hat j+3 hat k in...

    Text Solution

    |

  6. Statement 1 : Points A(1,0),B(2,3),C(5,3),a n dD(6,0) are concyclic. S...

    Text Solution

    |

  7. Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdo...

    Text Solution

    |

  8. Let vec a=a1 hat i+a2 hat j+a3 hat k , vec b=b1 hat i+b2 hat j+b3 hat...

    Text Solution

    |

  9. Statement-I A=2hat(i)+3hat(j)+6hat(k), B=hat(i)+hat(j)-2hat(k) and C=h...

    Text Solution

    |

  10. If vec a , vec b ,a n d vec c are mutually perpendicular vectors a...

    Text Solution

    |

  11. Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec ax...

    Text Solution

    |

  12. The number of vectors of unit length perpendicular to vectors vec ...

    Text Solution

    |

  13. Prove that ( vec a.hat i)( vec axx hat i)+( vec a.j)( vec axx hat j)+(...

    Text Solution

    |

  14. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

    Text Solution

    |

  15. If vec a is parallel to vec bxx vec c , then ( vec axx vec b).( vec ...

    Text Solution

    |

  16. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

    Text Solution

    |

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

    Text Solution

    |

  18. If |a|=2a n d|b|=3 and adotb=0,t h e n(axx(axx(axx(axxb)))) is equal t...

    Text Solution

    |

  19. If the two diagonals of one its faces are 6 hat i+6 hat ka n d4 hat ...

    Text Solution

    |

  20. The volume of a tetrahedron formed by the coterminous edges vec a ...

    Text Solution

    |