Home
Class 12
MATHS
if vecr.veci=vecr.vecj=vecr.veck and|vec...

if `vecr.veci=vecr.vecj=vecr.veck and|vecr|= 3, "then find vector" vecr`.

Text Solution

Verified by Experts

let `vecr= x hati+ yhatj+ zhatk`. Since `vecr.hati= vecr.Hatj = vecr.hatk`
x=y=z
Also `|vecr|= sqrt(x^(2)+y^(2)+z^(2))=3`
`x= sqrt3`
Hence, the required vector, `vecr= +-sqrt3(hati+hatj+hatk)`
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 vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and veca,vecb,vecc are non coplanar, then the area of the triangle whose vertices are A(veca),B(vecb) and C(vecc0 is (A) |[veca vecb vecc]| (B) |vecr| (C) |[veca vecb vecr]vecr| (D) none of these

If vecr.veca=0,vecr.vecb=0andvecr.vecc=0 for some non-zero vector vecr , then the value of veca.(vecbxxvecc) is…… .

If veca and vecb are mutually perpendicular unit vectors, vecr is a vector satisfying vecr.veca =0, vecr.vecb=1 and (vecr veca vecb)=1 , then vecr is:

If vecr.veca=vecr.vecb=vecr.vecc=0 for some non-zero vectro vecr , then the value of [(veca, vecb, vecc)] is

If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non-coplanar, then

Let veca=-hati-hatk,vecb =-hati + hatj and vecc = i + 2hatj + 3hatk be three given vectors. If vecr is a vector such that vecr xx vecb = vecc xx vecd and vecr.veca =0 then find the value of vecr .vecb .

Let veca=-hati-hatk, vecb=-hati+hatj and vecc=hati+2hatj+3hatk be three given vectors. If vecr is a vector such that vecrxxvecb=veccxxvecb and vecr.veca=0 , then the value of vecr.vecb is

If vecrxxvecb=veccxxvecb and vecr_|_veca then vecr is equal to

If veca, vecb, vecc are three non-coplanar vectors, then a vector vecr satisfying vecr.veca=vecr.vecb=vecr.vecc=1 , is

Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr.veca=0, |vecrxxvecb|=|vecr||vecb|,|vecrxxvecc|=|vecr||vecc| then [(veca, vecb, vecc)]=

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. if vecr.veci=vecr.vecj=vecr.veck and|vecr|= 3, "then find vector" vecr...

    Text Solution

    |

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

    Text Solution

    |

  3. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|v...

    Text Solution

    |

  4. If the vectors A ,B ,C of a triangle A B C are (1,2,3),(-1,0,0),(0,1,2...

    Text Solution

    |

  5. If |veca|=3, |vecb|=4 and the angle between veca and vecb is 120^(@) ....

    Text Solution

    |

  6. If vectors hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk are orthogon...

    Text Solution

    |

  7. Let veca vecb and vecc be pairwise mutually perpendicular vectors, suc...

    Text Solution

    |

  8. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

    Text Solution

    |

  9. If the angle between unit vectors veca and vecb is 60^(@) . Then find ...

    Text Solution

    |

  10. Let vecu=hai+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn is...

    Text Solution

    |

  11. A , B , C , D are any four points, prove that vec A Bdot vec C D+ ...

    Text Solution

    |

  12. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection...

    Text Solution

    |

  13. If the vectors 3vecP+vecq, 5vecP - 3vecq and 2 vecp+ vecq, 4 vecp - 2v...

    Text Solution

    |

  14. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

    Text Solution

    |

  15. Let veca , vecb and vecc be unit vectors such that veca+vecb+vecc=vecx...

    Text Solution

    |

  16. If veca and vecb are unit vectors, then find the greatest value of |ve...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |