Home
Class 12
MATHS
Find |veca| and |vecb| if (veca+vecb).(v...

Find `|veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |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 Question Bank|23 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

Similar Questions

Explore conceptually related problems

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

If |veca|=|vecb| , then (veca+vecb).(veca-vecb) is equal to

|veca pm vecb|^2 = |veca|^2 + |vecb|^2 pm 2|veca||vecb|cos theta and (veca + vecb).(veca - vecb) = |veca|^2 - |vecb|^2

Prove that: |(veca+vecb)xx(veca-vecb)|=2ab if veca_|_vecb

If |veca+vecb|=|veca-vecb| show that veca_|_vecb .

Find veca.vecb if |veca|2, |vecb|=5,a and |vecaxxvecb|=8

If |veca + vecb| =60 |veca-vecb|=40 and |vecb| = 46 find |veca|

Show that (veca xx vecb)^(2) = |veca| ^(2) |vecb|^(2) - (veca.vecb)^(2) = |(veca.veca)/(veca. vecb)(veca.vecb)/(vecb.vecb)|

If veca=4veci-3vecj and vecb=6veci+8vecj , find the magnitude and direction of veca , of vecb , of veca+vecb and of veca-vecb

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 P(1)=hati-hatj+hatk, P(2)= -hati+2hatj-hatik and P(3)=...

    Text Solution

    |

  3. Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |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. Find veca.vecb if |veca|2, |vecb|=5,a and |vecaxxvecb|=8

    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. I the vectors veca,veca=xhati+yhatj+zhatka and vecb=hatj are such that...

    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)=2vecaxx vecb and give a genometrica...

    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. Let veca vecb and vecc be three non-zero vectors such that veca + vecb...

    Text Solution

    |

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

    Text Solution

    |

  16. Let vea, vecb and vecc be unit vectors such that veca.vecb=0 = veca.ve...

    Text Solution

    |

  17. If |vecaxxvecb|^(2)+(veca.vecb)^(2)=144and|veca|=4,"then "|vecb| is eq...

    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

    |