Home
Class 12
MATHS
If veca and vecb be two non-collinear un...

If `veca and vecb` be two non-collinear unit vectors such that `vecaxx(vecaxxvecb)=1/2vecb` then find the angle between `veca and vecb`.

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|Exercise Exercise|337 Videos
  • DETERMINANTS

    CENGAGE|Exercise Question Bank|23 Videos
  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

Similar Questions

Explore conceptually related problems

If veca, vecb, vecc are non-coplanar unit vectors such that vecaxx(vecbxxvecc)=(vecb+vecc)/(sqrt(2)) then the angle between veca and vecb is

If veca and vecb are two vectors such that |veca xx vecb|= veca.vecb , then what is the angle between veca and vecb ?

If sqrt3|vecAxx vecB|= vecA*vecB , then find the angle between vecA and vecB .

If veca and vecb are unit vectors such that (veca +vecb). (2veca + 3vecb)xx(3veca - 2vecb)=vec0 then angle between veca and vecb is

If veca and vecb asre two vectors such that |veca|=2, |vecb| = 7 and vecaxxvecb=3hati+6hatk find the angle between veca and vecb

If veca,vecb are two unit vectors such that |veca + vecb| = 2sqrt3 and |veca -vecb|=6 then the angle between veca and vecb , is

Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(veca.vecb)vecb and vec=vecaxxvecb , then |vecv| is

If veca and vecb are two non collinear unit vectors and |veca+vecb|= sqrt3 , then find the value of (veca- vecb)*(2veca+ vecb)

If veca and vecb are two non collinear unit vectors and iveca+vecbi=sqrt(3) then find the value of (veca-vecb).(2veca+vecb)

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. prove that (veca.(vecbxxhati)hati(veca.(vecbxxhatj))hatj+ (veca.(vecbx...

    Text Solution

    |

  2. for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecax...

    Text Solution

    |

  3. If veca and vecb be two non-collinear unit vectors such that vecaxx(ve...

    Text Solution

    |

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

    Text Solution

    |

  5. Let veca,vecb and vecc be the non zero vectors such that (vecaxxvecb)x...

    Text Solution

    |

  6. If vecp, vecq , vecr denote vectors vecbxxvecc, vecc xx vecc xx veca, ...

    Text Solution

    |

  7. Let veca, vecb , vecc be non -coplanar vectors and let equations veca'...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati + b(2)hatj + b(3)hat...

    Text Solution

    |

  11. If |{:((a-x)^(2),(a-y)^(2),(a-z)^(2)),((b-x)^(2),(b-y)^(2),(b-z)^(2)),...

    Text Solution

    |

  12. OABC is a tetrahedron where O is the origin and A,B,C have position ve...

    Text Solution

    |

  13. Let k be the length of any edge of a regular tetrahedron (a tetrahe...

    Text Solution

    |

  14. In A B C , a point P is taken on A B such that A P//B P=1//3 and poin...

    Text Solution

    |

  15. Let O be an interior point of DeltaABC such that bar(OA)+2bar(OB) + ...

    Text Solution

    |

  16. The lengths of two opposite edges of a tetrahedron of aa n db ; the...

    Text Solution

    |

  17. Find the volume of a parallelopiped having three coterminus vectors of...

    Text Solution

    |

  18. Let vecp and vecq any two othogonal vectors of equal magnitude 4 each....

    Text Solution

    |

  19. Given that vecA,vecB,vecC form triangle such that vecA=vecB+vecC. Find...

    Text Solution

    |

  20. A line l is passing through the point vecb and is parallel to vector v...

    Text Solution

    |