Home
Class 12
MATHS
If |veca|=2 and |vecb|=3 and veca.vecb=0...

If `|veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(vecaxx(vecaxxvecb))))` is equal to the given diagonal is `vecc = 4 hatk = 8hatk` then , the volume of a parallelpiped is

A

`48 hatb`

B

`-48 hatb`

C

`48 hata`

D

`-48 hata`

Text Solution

Verified by Experts

The correct Answer is:
a
`(vecaxx (veca xx (veca xx (vecaxx vecb ))))`
` = (vecaxx (veca xx ((veca .vecb)veca -(veca .vecb)vecb)))`
`(veca xx (veca xx (-4vecb)))`
` -4 (veca xx (veca xx vecb))`
` -4 ((veca xx vecb) veca - (veca.veca)vecb)`
` -4 (-4vecb) = 16 vecb = 48 vecb`
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|=2, |vecb|=5 and veca*vecb=0 , then veca xx (vecaxx(vecaxx(vecaxx(vecaxx(veca xx vecb))))) is equal to :

If |veca|=and |vecb|=3 and veca.vecb=0 ,then (veca(vecx(vecaxx(vecaxx))))= (A) 48hatb (B) -48hatb (C) 48hata (D) -48hata

If the vectors veca and vecb are mutually perpendicular, then vecaxx{vecaxx{vecaxx(vecaxxvecb)}} is equal to

If veca,vecb and vecc are coplaner, then what is (2vecaxx3vecb).4vecc+(5vecbxx3vecc).6veca equal to?

Find the value of (veca+vecb)xx[vecaxx((veca-vecb)xxvecb)]

If vecaxx(vecbxxvecc)=vecbxx(veccxxveca) and [(vec, vecb, vecc)]!=0 then vecaxx(vecbxxvecc) is equal to

Prove that vecaxx(vecb+vecc)+vecbxx(vecc+veca)+veccxx(veca+vecb)=0

Prove that: vecaxx[vecbxx(veccxxveca)]=(veca.vecb)(vecaxxvecc)

Let |veca|=3, |vecb|=4, |vecc|=5 and vecaxx(vecaxxvecc)+4vecb=0 , then the value of |veca xx vecc|^(2) equals to

If veca=hati+hatj+hatk, veca.vecb=1 and vecaxxvecb=hatj-hatk then vecb

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

    Text Solution

    |

  2. If vecd=vecaxxvecb+vecbxxvecc+veccxxveca is a on zero vector and |(vec...

    Text Solution

    |

  3. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

    Text Solution

    |

  4. If two diagonals of one of its faces are 6hati + 6 hatk and 4 hatj + ...

    Text Solution

    |

  5. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

    Text Solution

    |

  6. If veca ,vecb and vecc are three mutually orthogonal unit vectors , th...

    Text Solution

    |

  7. vector vecc are perpendicular to vectors veca= (2,-3,1) and vecb= (1,...

    Text Solution

    |

  8. Given veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, ve...

    Text Solution

    |

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

    Text Solution

    |

  10. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

    Text Solution

    |

  11. If veca, vecb and vecc are such that [veca vecc vecc] =1, vecc= lambda...

    Text Solution

    |

  12. If 4veca+5vecb+9vecc=0 " then " (vecaxxvecb)xx[(vecbxxvecc)xx(veccxxve...

    Text Solution

    |

  13. Value of [vec a xx vec b,vec a xx vecc,vec d] is always equal to

    Text Solution

    |

  14. Let hata and hatb be mutually perpendicular unit vectors. Then for an...

    Text Solution

    |

  15. Let veca and vecb be unit vectors that are perpendicular to each other...

    Text Solution

    |

  16. veca and vecb are two vectors such that |veca|=1 ,|vecb|=4 and veca. V...

    Text Solution

    |

  17. Then for any arbitary vector veca, (((veca xx vecb) + (veca xx vecb))...

    Text Solution

    |

  18. If veca .vecb =beta and veca xx vecb = vecc ," then " vecb is

    Text Solution

    |

  19. If a(vecalphaxxvecbeta)=b(vecbetaxxvecgamma)+c(vecgammaxxvecalpha)=vec...

    Text Solution

    |

  20. If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non z...

    Text Solution

    |