Home
Class 11
MATHS
If veca is parallel to vecb xx vecc, the...

If `veca` is parallel to `vecb xx vecc, then (veca xx vecb) .(veca xx vecc) ` is equal to

A

`|veca|^(2)(vecb.vecc)`

B

`|vecb|^(2)(veca .vecc)`

C

`|vecc|^(2)(veca.vecb)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
` (veca xx vecb) . (veca xx vecc) = (veca xx vecb) . Vecu, " where " vecu = vecaxx vecc`
` Rightarrow veca. (vecb xx vecu) = veca. [vecb xx (veca xx vecc)]`
`veca . [ (vecb.vecc) veca - (veca. Vecb)vec]`
`=veca . (vecb.vecc) veca ( veca. vecb =0)`
` |veca|^(2) (vecb.vecc)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Single Question)|28 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Multiple Question)|11 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.3|18 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1316 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|320 Videos

Similar Questions

Explore conceptually related problems

If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is perpendicular to veca xx (vecb xx vecc) , then the value of [ veca xx ( vecb xx vecc)] xx vecc is equal to

If vectors, vecb, vcec and vecd are not coplanar, the pove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

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

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

For any four vectors veca, vecb, vecc, vecd the expressions (vecb xx vecc).(veca xx vecd) +(vecc xx veca).(vecb xx vecd)+(veca xx vecb).(vecc xx vecd) is always equal to:

if veca + vecb + vecc=0 , then show that veca xx vecb = vecb xx vecc = vecc xx veca .

Then for any arbitary vector veca, (((veca xx vecb) + (veca xx vecb))xx (vecb xx vecc)) (vecb -vecc) is always equal to

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D a...

    Text Solution

    |

  2. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

    Text Solution

    |

  3. If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vec...

    Text Solution

    |

  4. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |