Home
Class 11
MATHS
If vec a and vec b be two non-collinear...

If ` vec a` and `vec b` be two non-collinear unit vector such that ` vec axx( vec axx vec b)=1/2 vec b ,` then find the angle between ` vec a` and `vec b`.

Text Solution

Verified by Experts

`vecaxx (vecaxxvecb) =1/2 vecb Rightarrow(veca.vecb)veca-(veca.veca) vecb= 1/2vecb`
`Rightarrrow veca.vecb = 0 , veca. Veca = -1/2 ` ( which is not possible).
thus, the given information is inconsistent.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise single correct answer type|28 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.2|15 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE PUBLICATION|Exercise All Questions|689 Videos

Similar Questions

Explore conceptually related problems

If vec a , vec b and vec c are non-coplanar unit vectors such that vec axx( vec bxx vec c)=( vec b+ vec c)/(sqrt(2)) , then the angle between vec a and vec b is a. 3pi//4 b. pi//4 c. pi//2 d. pi

If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot

If three unit vectors vec a , vec b , and vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec a and vec bdot

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 .

If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 vec a+3 vec b)xx(3 vec a-2 vec b)]=0 , then angle between veca and vec b is

If vec a and vec b are unequal unit vectors such that ( vec a- vec b)xx[( vec b+ vec a)xx(2 vec a+ vec b)]= vec a+ vec b , then angle theta between vec aa n d vec b is 0 b. pi//2 c. pi//4 d. pi

If vec a,vec b are two vectors such that vec a.vec b <0 and |vec a.vec b| = |vec axxvec b| then the angle between vec a and vec b is

Two vectors vec(a) and vec (b) are such that |vec(a).vec(b)| = |vec(a) xx vec(b)| , then find the angle between the vectors vec(a) and vec(b) .

Let vec aa n d vec b be two non-collinear unit vector. If vec u= vec a-( vec adot vec b) vec ba n d vec v= vec axx vec b ,t h e n| vec v| is a. | vec u| b. | vec u|+| vec udot vec a| c. | vec u|+| vec udot vec b| d. | vec u|+ hat udot| vec a+ vec b|

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec a dot vec x=1, vec b dot vec x=3/2,| vec x|=2. Then find the angle between vec c and vec x

CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise 2.3
  1. If veca , vecb , vecc and vecd are four non-coplanar unit vectors such...

    Text Solution

    |

  2. If vecl,vecm,vecn are three non coplanar vectors prove that [vec vecm ...

    Text Solution

    |

  3. If the volume of a parallelepiped whose adjacent edges are vec a=2...

    Text Solution

    |

  4. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

    Text Solution

    |

  5. If vecx . Veca =0, vecx. Vecb=0 and vecx. vecc=0 for some non-zero vec...

    Text Solution

    |

  6. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

    Text Solution

    |

  7. If vec a , vec b, and vec c are three vectors such that vec axx ve...

    Text Solution

    |

  8. If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove...

    Text Solution

    |

  9. Prove that (veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vec...

    Text Solution

    |

  10. For any four vectors, vec a , vec b , vec c and vec d prove that vec...

    Text Solution

    |

  11. If vec a and vec b be two non-collinear unit vector such that vec ...

    Text Solution

    |

  12. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

    Text Solution

    |

  13. If vec a , vec b , and vec c be non-zero vectors such that no two ...

    Text Solution

    |

  14. If vec p , vec q , vec r denote vector vec bxx vec c , vec cxx vec a...

    Text Solution

    |

  15. Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the...

    Text Solution

    |

  16. Given unit vectors hatm hatn and hatp such that angle between hatm and...

    Text Solution

    |

  17. vec a , vec b ,a n d vec c are three unit vectors and every two are...

    Text Solution

    |

  18. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

    Text Solution

    |