Home
Class 12
MATHS
The pairs vec a,vec b and vec c,vec d ea...

The pairs `vec a,vec b` and `vec c,vec d` each determines plane. Then the planes are parallel if

A

`(vec(a) xx vec(c)) xx (vec(b) xx vec(d)) = 0`

B

`(vec(a) xx vec(c)).(vec(b) xx vec(d)) = vec(0)`

C

`(vec(a) xx vec(b)) xx (vec(c) xx vec(d)) = vec(0)`

D

`(vec(a) xx vec(b)).(vec(c) xx vec(d)) = vec(0)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • VECTOR

    MOTION|Exercise EXERCISE - 2 ( LEVEL -I)|21 Videos

  • VECTOR

    MOTION|Exercise EXERCISE - 2 ( LEVEL -II)|15 Videos

  • VECTOR

    MOTION|Exercise EXERCISE - 4 ( LEVEL-II)|41 Videos

  • TRIGONOMETRIC EQUATION

    MOTION|Exercise EXERCISE 4|10 Videos

Similar Questions

Explore conceptually related problems

Let the pairs a,b and c,d each determine a plane.Then the planes are parallel if (vec a xxvec c)xx(vec b xxvec d)=vec 0 b.(vec a xxvec c)*(vec b xxvec d)=vec 0 c.(vec a xxvec b)xx(vec c xxvec d)=vec 0d(vec a xxvec b)*(vec c xxvec d)=vec 0

Let the vector vec a,vec b,vec c,vec c,vec d be such that (vec a xxvec b)xx(vec c xxvec d)=vec 0. Let P_(1), and P_(2), be planes determined by the vectors vec a,vec b and vec c,vec d respectively.Then the angle between P_(1), and P_(2), is

Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec axx vec b)xx( vec cxx vec d)=0. Let P_1a n dP_2 be planes determined by the pair of vectors vec a , vec b ,a n d vec c , vec d , respectively. Then the angle between P_1a n dP_2 is a.0 b. pi//4 c. pi//3 d. pi//2

Volume of parallelepiped determined by vectors vec a,vec b and vec c is 5. Then the volume of the parallelepiped determined by vectors 3(vec a+vec b),(vec b+vec c) and 2(vec c+vec a) is

If vec a , vec b , vec c , vec d are non-zero, non collinear vectors and if ( vec ax vec b)x( vec cx vec d)dot( vec ax vec d)=0 , then which of the following is always true. vec a , vec b , vec c , vec d are necessarily coplanar either vec a or vec d must lie in the plane of vec b and vec c either vec b or vec c must lie in plane of vec a and vec d either vec a or vec b must lie in plane of vec c and vec d

If a vector vec a is perpendicular to two non- collinear vector vec b and vec c ,then vec a is perpendicular to every vector in the plane of vec b and vec c.

If vec c=2vec a+3vec b and 3vec c=3vec a-4vec b show that (i)vec c and vec a are like parallel and |vec c|>|vec a|( ii) vec c and vec b are unlike parallel and |vec c|>5|vec b|

vec axx( vec bxx vec c) , vec bxx( vec cxx vec a) and vec cxx( vec axx vec b) are: linearly dependent (b) coplanar vector parallel vectors (d) non coplanar vectors

If (vec a xxvec b)xx(vec c xxvec d)*(vec a xxvec d)=0 then which of the following may be true? vec a,vec b,vec c and vec d are necessarily coplanar b.vec a lies in the plane of vec c and vec d c.vec b lies in the plane of vec a and vec d d.vec c lies in the plane of vec a and vec d

36. If vec a, vec b, vec c and vec d are unit vectors such that (vec a xx vec b) .vec c xx vec d = 1 and vec a.vec c = 1/2 then a) vec a, vec b and vec c are non-coplanar b) vec b, vec c, vec d are non -coplanar c) vec b, vecd are non parallel d) vec a, vec d are parallel and vec b, vec c are parallel

MOTION-VECTOR -EXERCISE - 1
  1. Find the vector of length 3 unit which is perpendicular to hat i+ ...

    Text Solution

    |

  2. Given the vertices A(2,3,1), B(4,1,-2), C(6,3,7) and D(-5,-4,8) of a ...

    Text Solution

    |

  3. For a non zero vector vec(A) . If the equations vec(A).vec(B) = vec...

    Text Solution

    |

  4. If vecu and vecv are unit vectors and theta is the acute angle bet...

    Text Solution

    |

  5. If vecu=veca-vecb,vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvecv...

    Text Solution

    |

  6. If A(1,1,1),C(2,-1,2) the vector equation of the line vec(AB) is v...

    Text Solution

    |

  7. The value of [(veca -2vecb-vecc)(veca-vecb)( veca-vecb-vecc)] is equal...

    Text Solution

    |

  8. The volume of the parallelopiped constructed on the diagonals of the f...

    Text Solution

    |

  9. If vec u , vec va n d vec w are three non-cop0lanar vectors, then ...

    Text Solution

    |

  10. Let overset(to)(a) =a(1) hat(i) + a(2) hat(j) + a(3) hat(k) , overse...

    Text Solution

    |

  11. Vector vec x satisfying the relation vec A . vec x = c and vec B xx v...

    Text Solution

    |

  12. If vec a , vec b ,a n d vec c be non-zero vectors such that no tow...

    Text Solution

    |

  13. The pairs vec a,vec b and vec c,vec d each determines plane. Then the ...

    Text Solution

    |

  14. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

    Text Solution

    |

  15. If veca,vecb,vecc are linearly independent vectors, then which one of ...

    Text Solution

    |

  16. A point taken on each median of a triangle divides the median in the r...

    Text Solution

    |

  17. If G is the centroid of triangle A B C ,t h e n vec G A+ vec G B+ vec ...

    Text Solution

    |

  18. The vector bar(AB)=3hati+4hatk and bar(AC)=5hati-2hatj+4hatk are the s...

    Text Solution

    |

  19. If the vectors vec aa n d vec b are linearly idependent satisfying (s...

    Text Solution

    |

  20. If vec a , vec ba n d vec c are three mutually perpendicular vecto...

    Text Solution

    |