Home
Class 12
MATHS
For non zero vectors veca,vecb, vecc |...

For non zero vectors `veca,vecb, vecc`
`|(vecaxxvecb).vec|=|veca||vecb||vecc|` holds iff

A

`veca.vecb=0 , vecb .vecc=0`

B

`vecb.vecc = 0, vecc, veca =0`

C

`vecc.veca =0, veca,vecb =0`

D

`veca.vecb= vecb.vecc= vecc.veca =0`

Text Solution

Verified by Experts

The correct Answer is:
d
`|(veca xx vecb).vecc|=|veca||vecb||vecc|`
`or||veca||vecb|sin theta cos alpha|=|veca||vecb||vecc|`
` or |sinstheta||cos alpha|=1`
`Rightarrow theta=pi//2 and alpha=0`
` Rightarrow veca bot vecband vecc||hatn`
or perpendicular to both `veca and vecb`
`Rightarrow veca.vecb=vecb.vecc=vecc.veca=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

For non zero vectors veca,vecb,vecc|(vecaxxvecb).vecc|=|veca||vecb||vec| holds if and only if (A) veca.vecb=0,vecb.vecc=0 (B) vecb.vecc=0,vecc.veca=0 (C) vecc.veca=0,veca.vecb=0 (D) veca.vecb=vecb.vecc=vecc.veca=0

For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc = |veca||vecb||vecc| holds if and only if

Statement 1: If V is the volume of a parallelopiped having three coterminous edges as veca, vecb , and vecc , then the volume of the parallelopiped having three coterminous edges as vec(alpha)=(veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc vec(beta)=(veca.vecb)veca+(vecb.vecb)vecb+(vecb.vecc)vecc vec(gamma)=(veca.vecc)veca+(vecb.vecc)vecb+(vecc.vecc)vecc is V^(3) Statement 2: For any three vectors veca, vecb, vecc |(veca.veca, veca.vecb, veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|=[(veca,vecb, vecc)]^(3)

For three vectors veca, vecb and vecc , If |veca|=2, |vecb|=1, vecaxxvecb=vecc and vecbxxvecc=veca , then the value of [(veca+vecb,vecb+vecc,vecc+veca)] is equal to

Let veca,vecb,vecc be three non-zero vectors such that [vecavecbvecc]=|veca||vecb||vecc| then

veca=2hati+hatj+2hatk, vecb=hati-hatj+hatk and non zero vector vecc are such that (veca xx vecb) xx vecc = veca xx (vecb xx vecc) . Then vector vecc may be given as

If veca, vecb, vecc are three non coplanar, non zero vectors then (veca.veca)(vecbxxvecc)+(veca.vecb)(veccxxveca)+(veca.vecc)(vecaxxvecb) is equal to

For three non - zero vectors veca, vecb and vecc , if [(veca, vecb , vecc)]=4 , then [(vecaxx(vecb+2vecc), vecbxx(vecc-3veca), vecc xx(3veca+vecb))] is equal to

veca,vecb,vecc are non zero vectors. If vecaxxvecb=vecaxxvecc and veca.vecb=veca.vecc then show that vecb=vecc .

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |