Home
Class 12
MATHS
If veca, vecb and vecc are unit coplanar...

If `veca, vecb and vecc` are unit coplanar vectors , then the scalar triple porduct `[2 veca -vecb" " 2vecb - vecc " "2vecc-veca] `is

A

0

B

1

C

`-sqrt3`

D

`sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
a

`veca vecb and vecc` are unit coplanar vectors, `2veca- vecb , 2vecb - 2vecc and 2vecc - veca` are also coplanar, vectors ], being a linear combination of `veca , vecb and vecc` thus ` [ 2 veca - vecb 2vecb - vecc 2vecc - 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

If veca, vecb and vecc are unit coplanar vectors, then the scalar triple product [(2veca-vecb, 2vecb-vecc, 2vecc-veca)]=

Let veca,vecb and vecc be three vectors. Then scalar triple product [veca vecb vecc] is equal to

If veca, vecb and vecc are unit coplanar vectors, then [(2veca-3vecb,7vecb-9vecc,10vecc-23veca)]

If veca, vecb and vecc 1 are three non-coplanar vectors, then (veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)] equals

If veca, vecb and vecc 1 are three non-coplanar vectors, then (veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)] equals

If veca,vecb and vecc are unit coplanar vectors, then [(2veca-3vecb,7vecb-9vecc,12vecc-23vecb)] is equal to

If veca, vecb and vecc are non-coplanar vectors, prove that the four points 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+ 6 vecc are coplanar.

If veca, vecb, vecc are non-coplanar vectors, prove that the following vectors are coplanar. (i) 3veca - vecb - 4vecc, 3veca - 2vecb + vecc, veca + vecb + 2vecc (ii) 5veca +6vecb + 7vecc, 7veca - 8vecb + 9vecc, 3veca + 20 vecb + 5vecc

If veca, vecb, vecc are non-null non coplanar vectors, then [(veca-2vecb+vecc, vecb-2vecc+veca, vecc-2veca+vecb)]=

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. The unit vector which is orthogonal to the vector 5hatj + 2hatj + 6hat...

    Text Solution

    |

  10. if veca , vecb and vecc are three non-zero, non- coplanar vectors and ...

    Text Solution

    |

  11. Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk and vecc= hati+hat...

    Text Solution

    |

  12. Lelt two non collinear unit vectors hata and hatb form and acute angle...

    Text Solution

    |

  13. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

    Text Solution

    |

  14. Two adjacent sides of a parallelogram A B C D are given by vec A B...

    Text Solution

    |

  15. Let P, Q, R and S be the points on the plane with position vectors -2h...

    Text Solution

    |

  16. Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj...

    Text Solution

    |

  17. Let bar(PR)=3hati+hatj-2hatk and bar(SQ)=hati-3hatj-4hatk determine d...

    Text Solution

    |

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

    Text Solution

    |

  19. The number of vectors of unit length perpendicular to vectors vec ...

    Text Solution

    |

  20. Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hat...

    Text Solution

    |