Home
Class 12
MATHS
Let hata and hatb be two unit vectors su...

Let `hata` and `hatb` be two unit vectors such that `hata.hatb=1/3` and `hata xx hatb=hatc`, Also `vecF=alphahata+betahatb+lambdahatc`,
where, `alpha,beta,lambda` are scalars. If `alpha=k_(1)(vecF.hata)-k_(2)(vecF.hatb)` then the value of `2(k_(1)+k_(2))` is

A

`2sqrt(3)`

B

`sqrt(3)`

C

`3`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise JEE Type Solved Examples: Passage Based Type Questions|3 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|12 Videos

  • PROBABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|54 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

Let hata, hatb and hatc be three unit vectors such that hata=hatb+(hatb xx hatc) , then the possible value(s) of |hata+hatb+hatc|^(2) can be :

Let hatu, hatv, hatw be three unit vectors such that hatu+hatv+hatw=hata, hata.hatu=3/2, hata.hatv=7/4 & |hata|=2 , then

Let hat a , hat b , hatc be unit vectors such that hat a * hatb =hat a *hatc =0 and the angle between hat b and hat c be (pi)/(6) prove that hat a =+- 2 (hatb xx hat c )

If hata, hatb, hatc are three units vectors such that hatb and hatc are non-parallel and hataxx(hatbxxhatc)=1//2hatb then the angle between hata and hatc is

If hata, hatb and hatc are non-coplanar unti vectors such that [hata hatb hatc]=[hatb xx hatc" "hatc xx hata" "hata xx hatb] , then find the projection of hatb+hatc on hata xx hatb .

If hata and hatb are unit vectors then the vector defined as vecV=(hata xx hatb) xx (hata+hatb) is collinear to the vector :

Let hata and hatb be mutually perpendicular unit vectors. Then for ant arbitrary vecr .

If hata" and "hatb are non-collinear unit vectors and if |hata+hatb|=sqrt(3) , then the value of (2hata-5hatb).(3hata+hatb) is :-

The angle between two vectors veca and vecb is pi//2 . Then |hata xx hatb| is

hata, hatb and hata-hatb are unit vectors. The volume of the parallelopiped, formed with hata, hatb and hata xx hatb as coterminous edges is :

ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let hata and hatb be two unit vectors such that hata.hatb=1/3 and hata...

    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 O X , O Y , O Z be three unit vectors ...

    Text Solution

    |

  5. Let a, b and c be three unit vectors such that atimes(btimesc)=(sqrt(3...

    Text Solution

    |

  6. Let vec a , vec b and vec c be three non-zero vectors such that no ...

    Text Solution

    |

  7. If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...

    Text Solution

    |

  8. The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...

    Text Solution

    |

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

    Text Solution

    |

  10. Two adjacent sides of a parallelogram A B C D are given by vec A B=...

    Text Solution

    |

  11. Let P,Q R and S be the points on the plane with position vectors -2hat...

    Text Solution

    |

  12. If aa n db are vectors in space given by vec a=( hat i-2 hat j)/(sq...

    Text Solution

    |

  13. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(...

    Text Solution

    |

  14. The edges of a parallelopiped are of unit length and are parallel to ...

    Text Solution

    |

  15. Let two non-collinear unit vectors veca and vecb form an acute angle. ...

    Text Solution

    |

  16. Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular...

    Text Solution

    |

  17. The number of distinct real values of lambda , for which the vectors...

    Text Solution

    |

  18. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

    Text Solution

    |

  19. Let vec A be a vector parallel to the line of intersection of plan...

    Text Solution

    |

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

    Text Solution

    |

  21. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

    Text Solution

    |