Home
Class 12
MATHS
If veca, vecb, vecc are three non-zero v...

If `veca, vecb, vecc` are three non-zero vectors, then which of the following statement(s) is/are true?

A

`atimes(btimesc), btimes(ctimesa), ctimes(atimesb)` form a right handed system

B

`c, (atimesb)times, atimesb` form a right handed system

C

`a*b+b*c+c*alt0, if a+b+c=0`

D

`((atimesb)*(btimesc))/((btimesc)*(atimesc))=-1, if a+b+c=0`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|12 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|73 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

Given three vectors veca, vecb and vecc are non-zero and non-coplanar vectors. Then which of the following are coplanar.

If veca, vecb and vecc are three non-zero vectors, no two of which are collinear, veca +2 vecb is collinear with vecc and vecb + 3 vecc is collinear with veca , then find the value of |veca + 2vecb + 6vecc| .

If veca, vecb and vecc are three non-zero, non-coplanar vectors,then find the linear relation between the following four vectors : veca-2vecb+3vecc, 2veca-3vecb+4vecc, 3veca-4vecb+ 5vecc, 7veca-11vecb+15vecc .

Let veca,vecb, and vecc be three non zero vector such that no two of these are collinear. If the vector veca+2vecb is collinear with vecc and vecb+3vecc is colinear with veca (lamda being some non zero scalar) then veca\+2vecb+6vecc equals (A) lamdaveca (B) lamdavecb (C) lamdavecc (D) 0

If veca, vecb, vecc are three non-zero non-null vectors are vecr is any vector in space then [(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb+[(veca, vecb, vecr)]vecc is equal to

If veca, vecb, vecc are three non-coplanar vectors, then a vector vecr satisfying vecr.veca=vecr.vecb=vecr.vecc=1 , is

If veca, vecb and vecc are three non-coplanar non-zero vectors, then prove that (veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)veca xx vecb = [vecb vecc veca] veca

If veca, vecb and vecc are three non-coplanar non-zero vectors, then prove that (veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)veca xx vecb = [vecb vecc veca] veca

If veca, vecb, vecc are three non-zero vectors such that veca + vecb + vecc=0 and m = veca.vecb + vecb.vecc + vecc.veca , then:

ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (More Than One Correct Option Type Questions)
  1. Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vecto...

    Text Solution

    |

  2. If veca and vecb are two unit vectors perpendicular to each other and...

    Text Solution

    |

  3. Given three non-coplanar vectors OA=a, OB=b, OC=c. Let S be the centre...

    Text Solution

    |

  4. If a=hat(i)+hat(j)+hat(k) and b=hat(i)-hat(j), then the vectors (a*hat...

    Text Solution

    |

  5. If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat ka n d...

    Text Solution

    |

  6. If veca, vecb, vecc are three non-zero vectors, then which of the foll...

    Text Solution

    |

  7. Let the unit vectors a and b be perpendicular and the unit vector c be...

    Text Solution

    |

  8. If veca, vecb, vecc are three non-zero vectors, then which of the foll...

    Text Solution

    |

  9. Let veca and vecb be two non- zero perpendicular vectors. A vector vec...

    Text Solution

    |

  10. If veca and vecb are any two unit vectors, then find the greatest post...

    Text Solution

    |

  11. If vec a is perpendicular to vec b and vec r is non-zero vector suc...

    Text Solution

    |

  12. In a four-dimensional space where unit vectors along the axes are ...

    Text Solution

    |

  13. A vector(d) is equally inclined to three vectors a=hat(i)-hat(j)+hat(k...

    Text Solution

    |

  14. If a, b, c are non-zero, non-collinear vectors such that a vectors suc...

    Text Solution

    |

  15. Given three vectors veca, vecb and vecc are non-zero and non-coplanar ...

    Text Solution

    |

  16. If r=hat(i)+hat(j)+lambda(2hat(i)+hat(j)+4hat(k)) and r*(hat(i)+2hat(j...

    Text Solution

    |

  17. If vectors veca and vecb are two adjacent sides of parallelograsm then...

    Text Solution

    |

  18. Let a, b, c be three vectors such that each of them are non-collinear,...

    Text Solution

    |

  19. If a, b and c are non-collinear unit vectors also b, c are non-colline...

    Text Solution

    |

  20. If a=(1)/(7)(2hat(i)+3hat(j)+6hat(k)): b=(1)/(7)(6hat(i)+2hat(j)-3hat...

    Text Solution

    |