Home
Class 12
MATHS
Find |veca|and|vecb|, if (veca+vecb)*(ve...

Find `|veca|and|vecb|`, if `(veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|`.

Text Solution

Verified by Experts

`|veca+vecb|^(2)+|veca-vecb|^(2)= 2(|veca|^(2)+|vecb|^(2))`
`Rightarrow 100 + 64 = 2(25+|vecb|^(2))`
`or 82 = 25 + |vecb|^(2)`
`or |vecb|^(2) = 57`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DETERMINANTS

    CENGAGE|Exercise All Questions|268 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

Similar Questions

Explore conceptually related problems

For any two vectors veca and vecb prove that |vecaxxvecb|^(2)+(veca*vecb)^(2)=|veca|^(2)|vecb|^(2)

If |veca|=5|vecb|=4 and |veca+vecb|=1 then |veca-vecb|= ?

[veca, veca+vecb, veca+vecb+vecc] is :

Three vectors veca,vecb,vecc are such that veca xx vecb=4(veca xx vecc) and |veca|=|vecb|=1 and |vecc|=1/4 . If the angle between vecb and vecc is pi/3 then vecb is

If |veca|=5,|vecb|=6,|vecc|=7 and veca+vecb+vecc=vec0 , find veca.vecb+vecb.vecc+vecc.veca.

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc .

If |veca|=5 , |veca-vecb| = 8 and |veca +vecb|=10 then find |vecb|

If [ veca vecbvecc]=2 , then find the value of [(veca+2vecb-vecc) (veca - vecb) (veca - vecb-vecc)]

Find the angle between veca and vecb If |vecaxxvecb|=|veca.vecb| .

If veca and vecb are unequal unit vectors such that (veca - vecb) xx[ (vecb + veca) xx (2 veca + vecb)] = veca+vecb then angle theta " between " veca and vecb is

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca and vecb are unit vectors, then find the greatest value of |ve...

    Text Solution

    |

  2. Constant forces P1= hat i+ hat j+ hat k ,P2= hat i+2 hat j- hat ka n d...

    Text Solution

    |

  3. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

    Text Solution

    |

  4. If A ,B ,C ,D are four distinct point in space such that A B is not...

    Text Solution

    |

  5. If veca=2hati+ 3hatj-5hatk,vecb =m hati+nhatj +12 hatk and veca xx vec...

    Text Solution

    |

  6. If |veca|=2, |vecb|=5 and |vecaxxvecb|=8 then find the value of veca.v...

    Text Solution

    |

  7. If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are co...

    Text Solution

    |

  8. If veca = 2vecj+3vecj-veck, vecb =-veci+2vecj-4veck and vecc=veci + ve...

    Text Solution

    |

  9. if the vectors vecc, veca = xhati +yhatj + zhatk and vecb = hatj are s...

    Text Solution

    |

  10. given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca...

    Text Solution

    |

  11. Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb)

    Text Solution

    |

  12. If vec x and vecy are unit vectors and |vecz| = 2/sqrt7 such that vecz...

    Text Solution

    |

  13. prove that (veca.hati)(vecaxxhati)+(veca.hatj)(vecaxxhatj)+(veca.hatk)...

    Text Solution

    |

  14. If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c ...

    Text Solution

    |

  15. A particle has an angular speed of 3 rad/s and the axis of rotation...

    Text Solution

    |

  16. If veca,vecb,vecc be unit vectors such that veca.vecb=veca.vecc=0 and ...

    Text Solution

    |

  17. if (vecaxxvecb)^(2)+ (veca.vecb)^(2) = 144 and |veca|=4 the find the v...

    Text Solution

    |

  18. Given |veca|=|vecb|=1 and |veca + vecb|= sqrt3 "if" vecc is a vector s...

    Text Solution

    |

  19. Find the moment of vec F about point (2, -1, 3), where force vec ...

    Text Solution

    |

  20. If veca , vecb , vecc and vecd are four non-coplanar unit vectors such...

    Text Solution

    |