Home
Class 12
MATHS
Let vec r , vec a , vec b and vec c be ...

Let `vec r , vec a , vec b` and `vec c ` be four non zero vectors such that `vec r.vec a = 0, |vec r xx vecb|=|vecr||vecb| " and " |vec r xx vec c | = |vec r||vec c |` . Then [abc] is equal to

A

|a||b||c|

B

` - |a||b||c|

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    DISHA PUBLICATION|Exercise EXERCISE -1 : CONCEPT BUILDER|60 Videos

  • TRIGONOMETRIC FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE-2|30 Videos

Similar Questions

Explore conceptually related problems

Let vec r,vec a,vec b and vec c be four nonzero vectors such that vec r*vec a=0,|vec r xxvec b|=|vec r||vec b| and |vec r xxvec c|=|vec r||vec c| Then [abc] is equal to |a||b||c| b.-|a||b||c| c.0 d.none of these

Let vec a, vec b, vec c be three non-zero vectors such that [vec with bvec c] = | vec a || vec b || vec c | then

If vec P xx vec Q= vec R, vec Q xx vec R= vec P and vec R xx vec P = vec Q then

If [veca xx vecb vecb xx vec c vec c xx vec a] = lamda [veca vecb vec c ]^2 then lamda is equal to

If vec( a) , vec( b) , vec( c ) are non coplanar non-zero vectors such that vec( b) xxvec( c) = vec( a ), vec( a ) xx vec( b) =vec( c ) and vec( c ) xx vec( a ) = vec ( b ) , then which of the following is not true

If vec a, vec b, vec c are three vectors such that | vec b | = | vec c | then {(vec a + vec b) xx (vec a + vec c)} xx {(vec b xxvec c)} * (vec b + vec c) =

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0, then vec r is equal to

If vec a,vec b and vec c are three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0 then vec r is equal to

Let vec a , vec b ,vec c are three non- coplanar vectors such that vecr_(1)=veca + vec c , vecr_(2)= vec b+vec c -veca , vec r_(3) = vec c + vec a + vecb, vec r = 2 vec a - 3 vec b + 4 vec c. If vec r = lambda_(1)vecr_(1)+lambda_(2)vecr_(2)+lambda_(3)vecr_(3) , then

DISHA PUBLICATION-VECTOR ALGEBRA-EXERCISE -2 : CONCEPT APPLICATOR
  1. veca, vecb ,vec c are three vectors with magnitude |veca| = 4, |vecb|...

    Text Solution

    |

  2. If the two adjacent sides of two rectangles are represented by vect...

    Text Solution

    |

  3. OA, OB, OC are the sides of a rectangular parallelopiped whose diagona...

    Text Solution

    |

  4. If the positive numbers a, b and c are the pth, qth and rth terms of G...

    Text Solution

    |

  5. A vector veca=(x,y,z) makes an obtuse angle with F-axis, and make equa...

    Text Solution

    |

  6. Let vecOB = hati + 2hatj + 2hatk " and" vecOA = 4hati + 2hatj + 2hatk ...

    Text Solution

    |

  7. If a1 , a2 and a3 are three numbers satisfying a1^2 + a2^2 +a3^2 = 1 ,...

    Text Solution

    |

  8. Let veca , vecb and vec c be non coplanar unit vectors equally incl...

    Text Solution

    |

  9. Let veca , vecb, vec c be three non coplanar vectors , and let vecp ,...

    Text Solution

    |

  10. Let veca= 2hati+hatj -2hatk and vecb=hati+hatj. If vec c is a vecto...

    Text Solution

    |

  11. Let vec r , vec a , vec b and vec c be four non zero vectors such tha...

    Text Solution

    |

  12. Let vec r = (veca xx vecb) sin x + (vecb + vec c) cos y + 2 (vec c xx...

    Text Solution

    |

  13. A girl walks 4 km towards west, then she walks 3 km in a direction 30...

    Text Solution

    |

  14. If vec a+vec b+vec c=0, prove that (vec a xx vec b)=(vec b xx vec c)=(...

    Text Solution

    |

  15. If |vec a + vecb| = |vec a - vecb| , then which one of the following i...

    Text Solution

    |

  16. The resultant of forces vecP and vec Q is vecR . If vec Q is doubled t...

    Text Solution

    |

  17. If vec b is a vector whose initial point divides thejoin of 5 hat ...

    Text Solution

    |

  18. A body travels a distance s in t seconds. It starts from rest and ends...

    Text Solution

    |

  19. Two particles start simultaneously from the same point and move along ...

    Text Solution

    |

  20. vec p , vec q ,a n d vec r are three mutually perpendicular vectors of...

    Text Solution

    |