Home
Class 12
MATHS
Unit vector perpendicular to the plane o...

Unit vector perpendicular to the plane of `DeltaABC` with position vectors a,b,c of the vertices A,B,C is

A

`((vec(a) xx vec(b) + vec(b) xx vec(c) + vec(c) xx vec(a)))/(Delta)`

B

`((vec(a) xx vec(b) + vec(b) xx vec(c) + vec(c) xx vec(a)))/(2Delta)`

C

`((vec(a) xx vec(b) + vec(b) xx vec(c) + vec(c) xx vec(a)))/(4Delta)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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

(a) Prove that the normal to the plane containing three points whose position vectors are vec(a), vec(b), vec(c ) lie in the direction of vec(b)xx vec(c )+vec(c )xx vec(a)+vec(a)xx vec(b) . (b) Find the unit vector perpendicular to the plane ABC, where the position vectors of A, B and C are : 2hat(i)-hat(j)+hat(k), hat(i)+hat(j)+2hat(k) and 2hat(i)+hat(k) respectively.

What is the unit vector perpendicular to the plane of vectors A and B ?

Find a unit vector perpendicular to plane ABC when position vectors of A,B,C are 3 hati - hatj + 2hatk, hati - hatj- 3hatk and 4 hati - 3 hatj + hatk respectively.

A unit vector c perpendicular to a=i-j and coplanar with a and b=i+k is

If a=i+j-k,b=i-j+k and c is a unit vector perpendicular to the vector a and coplanar with a and b,then aunit vector d perpendicular to both a and c is

let a,b, and c be three unit vectors such that a is perpendicular to the plane off b and c. if the angle betweenn b annd c is (pi)/(3) , then |axxb-axxc| is equal to

MOTION-VECTOR -EXERCISE - 1
  1. Let vec a = hati+hatj and vec b = 2 hat i - hat k. The point of inters...

    Text Solution

    |

  2. Vectors aa n db make an angle theta=(2pi)/3dot If | vec a|=1,| vec b|=...

    Text Solution

    |

  3. Unit vector perpendicular to the plane of DeltaABC with position vecto...

    Text Solution

    |

  4. If vec(b) and vec(c) are two non-collinear vectors such that vec(a)...

    Text Solution

    |

  5. Find the vector of length 3 unit which is perpendicular to hat i+ ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |