Home
Class 12
MATHS
Let vec(a) , vec(b) and vec(c) be three ...

Let `vec(a)` , `vec(b)` and `vec(c)` be three non-zero vectors such that no two of them are collinear and `(vec(a)×vec(b))×vec(c)=1/3|vec(b)||vec(c)|vec(a)`. If `theta` is the angle between vectors `vec(b)` and `vec(c)`, then the value of `sintheta` is:

A

`(1)/(3)`

B

`(sqrt(2))/(3)`

C

`(2)/(3)`

D

`(2sqrt(2))/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|18 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

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

Similar Questions

Explore conceptually related problems

Let vec a,vec b and vec c be three non-zero vectors such that no two of them are collinear and (vec a xxvec b)xxvec c=(1)/(3)|vec b||vec c|vec a* If theta is the angle between vectors vec b and vec c, then the value of sin theta is:

Let vec a,vec b and vec c be three non-zero vectors such that no two of them are collinear and (vec a xxvec b)xxvec c=(1)/(3)|vec c||vec b||vec a|* If theta is the angle between vectors vec b and vec c then a value of sin theta is :

If vec a,vec b, and vec c be non-zero vectors such that no tow are collinear or (vec a xxvec b)xxvec c=(1)/(3)|vec b||vec c|vec a* If theta is the acute angle between vectors vec b and vec c, then find the value of sin theta.

If theta is angle between vec a and vec b and |vec a.vec b|=|vec a timesvec b| then find the value of theta

Let vec a, vec b, vec c be three non-zero vectors such that [vec with bvec c] = | vec a || vec b || vec c | then

Let vec a,vec b,vec c are three non-zero vectors and vec b is neither perpendicular to vec a nor to vec c and " (vec a timesvec b)timesvec c=vec a times(vec b timesvec c) .Then the angle between vec a and vec c is:

Let vec a,vec b,vec c be three non-zero vectors such that any two of them are non-collinear.If vec a+2vec b is collinear with vec c and vec b+3vec c is collinear with vec a then prove that vec a+2vec b+6vec c=vec 0

If vec(a), vec(b) and vec(c) are unit vectors such that vec(a)+2vec(b)+2vec(c)=0 then |vec(a)timesvec(c)| is equal to

vec a,vec b and vec c are three non-zero vectors,no two of which are collinear and the vectors vec a+vec b is collinear with vec b,vec b+vec c is collinear with vec a, then vec a+vec b+vec c=

ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let veca =hatj-hatk and vecc =hati-hatj-hatk. Then the vector b satisf...

    Text Solution

    |

  2. If the vectors veca=hati-hatj+2hatk.vecb=2hati+4hatj+hatk and veccc=la...

    Text Solution

    |

  3. If vecu, vecv, vecw are non -coplanar vectors and p,q, are real numbe...

    Text Solution

    |

  4. The vector vec a=""alpha hat i+2 hat j+""beta hat k lies in the pl...

    Text Solution

    |

  5. If vecu and vecv are unit vectors and theta is the acute angle bet...

    Text Solution

    |

  6. Let bar a= hat i+ hat j+ hat k ,""b= hat i- hat j+2 hat k and bar...

    Text Solution

    |

  7. If (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc), Where veca, vecb and vecc a...

    Text Solution

    |

  8. The values of a for which the points A, B, and C with position vectors...

    Text Solution

    |

  9. The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-...

    Text Solution

    |

  10. If veca is any vector, then (vec a xx vec i)^2+(vec a xx vecj)^2+(ve...

    Text Solution

    |

  11. If veca,vecb,vecc are non-coplanar vectors and lambda is a real number...

    Text Solution

    |

  12. If vec(a)=ht(i)-hat(k), vec(b)=xhat(i)+hat(j)+(1-x)hat(k) vec(c)=yha...

    Text Solution

    |

  13. Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

    Text Solution

    |

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

    Text Solution

    |

  15. A particle acted by constant forces 4 hat i+ hat j-3 hat ka n d3 ha...

    Text Solution

    |

  16. If bar u,bar v,bar w are three non coplanar vectors then (bar u+bar ...

    Text Solution

    |

  17. a, b, c are three vectors, such that a+b+c=0 |a|=1, |b|=2, |c|=3, then...

    Text Solution

    |

  18. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

    Text Solution

    |

  19. Let hat u= hat i+ hat j , hat v= hat i- hat ja n d hat w= hat i+2 hat...

    Text Solution

    |

  20. Given, two vectors are hat(i)-hat(j) and hat(i)+2hat(j), the unit vect...

    Text Solution

    |