Home
Class 12
MATHS
The scalar vecA.(vecB+vecC)xx(vecA+vecB+...

The scalar `vecA.(vecB+vecC)xx(vecA+vecB+vecC)` equals (A) 0 (B) `[vecA vecB vecC]+[vecB vecC vecA]` (C) `[vecA vecB vecC]` (D) none of these

A

0

B

`[vecA vecB vecC]+ [vecB vecC vecA] `

C

`[vecA vecB vecC]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
`vecA.(vecB + vecC) xx (vecA + vecB +vecC)`
` vecA . ([vecB xx vecA +vecB xx vecB + vecC + vecC xx vecA + vecC xx vecB +vecC xx vecC]`
`= vecA.vecBxxvecA + vecA.vecBxxvecC+vecA.vecCxx vecA + vecA+ vecC xx vecB " " ( "using" veca xx veca =0)`
`0+[vecA vecB vecC]+0+ [vecA vecC vecB]`
`[vecA vecB vecC]-[vecA vecB vecC]`
=0
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 and vecC are three non coplanar then (vecA+vecB+vecC).{(vecA+vecB)xx(vecA+vecC)} equals: (A) 0 (B) [vecA, vecB, vecC] (C) 2[vecA, vecB,vecC] (D) -[vecA,vecB,vecC]

The value of veca.(vecb+vecc)xx(veca+vecb+vecc) , is

If vecA + vecB + vecC = vec0 , then vecA.(vecB xx vecC) = ……….

If vecA + vecB +vecC = 0 , then vecA xx vecB is

If veca,vecb,vecc are unity vectors such that vecd=lamdaveca+muvecb+gammavecc then gamma is equal to (A) ([veca vecb vecc])/([vecb veca vecc]) (B) ([vecb vecc vecd])/([vecb vecc veca]) (C) ([vecb vecd vecc])/([veca vecb vecc]) (D) ([vecc vecb vecd])/([veca vecb vecc])

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of [veca\' vecb\' vecc\']^-1 is (A) 2[veca vecb vecc] (B) [veca,vecb,vecc] (C) 3[veca vecb vecc] (D) 0

If vecA=(vecbxxvecc)/([vecb vecc vecc]), vecB=(veccxxveca)/([vecc veca vecb)], vecC=(vecaxxvecb)/([veca vecb vecc)] find [vecA vecB vecC]

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of (vecaxxveca\')+(vecbxxvecb)+(vecccxxveccc\') is (A) veca+vecb+vec (B) veca\'+vecb\'+vec\' (C) 0 (D) none of these

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

If vecc=vecaxxvecb and vecb=veccxxveca then (A) veca.vecb=vecc^2 (B) vecc.veca.=vecb^2 (C) veca_|_vecb (D) veca||vecbxxvecc

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If vecx.veca=0vecx.vecb=0 and vecx.vecc=0 for some non zero vector vec...

    Text Solution

    |

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

    Text Solution

    |

  3. The scalar vecA.(vecB+vecC)xx(vecA+vecB+vecC) equals (A) 0 (B) [vecA v...

    Text Solution

    |

  4. For non zero vectors veca,vecb, vecc |(vecaxxvecb).vec|=|veca||vecb|...

    Text Solution

    |

  5. The volume of he parallelepiped whose sides are given by vec O A=2...

    Text Solution

    |

  6. Let veda,vecb,vecc be three noncolanar vectors and vecp,vecq,vecr are ...

    Text Solution

    |

  7. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

    Text Solution

    |

  8. If veca,vecb and vecc are non coplanar and unit vectors such that veca...

    Text Solution

    |

  9. Let vecu,vecv and vecw be vectors such that vecu+ vecv + vecw =0 if |v...

    Text Solution

    |

  10. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

    Text Solution

    |

  11. Let vecp,vecq, vecr be three mutually perpendicular vectors of the sam...

    Text Solution

    |

  12. Let veca = 2i + j -2k, and b = i+ j if c is a vector such that veca ....

    Text Solution

    |

  13. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

    Text Solution

    |

  14. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

    Text Solution

    |

  15. Let the vectors veca, vecb,vecc and vecd be such that (vecaxxvecb)xx(v...

    Text Solution

    |

  16. If veca, vecb and vecc are unit coplanar vectors , then the scalar tri...

    Text Solution

    |

  17. if hata, hatb and hatc are unit vectors. Then |hata - hatb|^(2) + |hat...

    Text Solution

    |

  18. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

    Text Solution

    |

  19. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

    Text Solution

    |

  20. The value of a so thast the volume of parallelpiped formed by vectors ...

    Text Solution

    |