Home
Class 12
MATHS
A , B , Ca n dD are any four points in t...

`A , B , Ca n dD` are any four points in the space, then prove that `| vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4` (area of ` A B C` .)

A

`2Delta`

B

`4Delta`

C

`3Delta`

D

`5Delta`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    VMC MODULES ENGLISH|Exercise LEVEL -2|47 Videos
  • VECTORS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos
  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE) (TRUE/ FALSE)|30 Videos
  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

If A ,B ,C ,D be any four points in space, prove that | vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4 (Area of triangle ABC)

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=4(Area \ of triangle ABC).

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=0.

A B C D E is pentagon, prove that vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

A,B,C,D are four points in the space and satisfy | vec A B|=3,| vec B C|=7,| vec C D|=11&| vec D A|=9 , then value of vec (AC). vec(BD) .

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Prove that [ vec a , vec b , vec c+ vec d]=[ vec a , vec b , vec c]+[ vec a , vec b , vec d]

If veca , vec b , vec c are three vectors such that veca+ vec b+ vec c= vec0 , then prove that vec axx vec b= vec bxx vec c= vec cxx vec a

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the equation vec a^' , vec b^' , vec c ' are reciprocal system of vector vec a , vec b , vec c , then prove that vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c ' is a null vector.

VMC MODULES ENGLISH-VECTORS -LEVEL -1
  1. If vece(1) = ( 1,1,1) and vece(2) = ( 1,1,-1) and veca and vecb are tw...

    Text Solution

    |

  2. The length of the longer diagonal of the parallelogram constructed on ...

    Text Solution

    |

  3. A , B , Ca n dD are any four points in the space, then prove that |...

    Text Solution

    |

  4. Let vec O A= vec a , vec O B=10 vec a+2 vec b ,a n d vec O C=bw h e r...

    Text Solution

    |

  5. ABCDEF is a regular hexagon with centre a the origin such that vec(AB)...

    Text Solution

    |

  6. ABCD a parallelogram, and A1 and B1 are the midpoints of sides BC and ...

    Text Solution

    |

  7. The vertices of a triangle have the position vectors veca,vecb,vecc an...

    Text Solution

    |

  8. If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc...

    Text Solution

    |

  9. Vectors veca,vecb and vecc are of the same length and when taken pair-...

    Text Solution

    |

  10. If three vectors veca, vecb,vecc are such that veca ne 0 and veca xx v...

    Text Solution

    |

  11. veca,vecb,vecc are three non-coplanar vectors such that veca+vecb+vecc...

    Text Solution

    |

  12. If S is the cirucmcentre, G the centroid, O the orthocentre of a trian...

    Text Solution

    |

  13. If veca, vecb, vecc are three non-zero vectors such that veca + vecb +...

    Text Solution

    |

  14. Let alpha,beta and gamma be distinct real numbers. The points with pos...

    Text Solution

    |

  15. If |veca|=4, |vecb|=4 and |vecc|=5 such that veca bot vecb + vecc, vec...

    Text Solution

    |

  16. If vecu=veca-vecb, vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvec...

    Text Solution

    |

  17. If the vectors vecc, \ veca=xhati+yhatj+zhatk and vecb=hatj are such ...

    Text Solution

    |

  18. Given any vector, vecr,|vecr xx hati|^(2) + |vecr xx hatj|^(2) + |vecr...

    Text Solution

    |

  19. The value of x fot which the angle between the vectors a=-3hat(i)+xhat...

    Text Solution

    |

  20. If a,b and c are non-coplanar vectors and lamda is a real number, then...

    Text Solution

    |