Home
Class 12
MATHS
Let vec a , vec b ,a n d vec ca n d vec...

Let ` vec a , vec b ,a n d vec ca n d vec a^' , vec b^' , vec c '` are reciprocal system of vectors, then prove that ` vec a^'xx vec b^'+ vec b^'xx vec c^'+ vec c^'xx vec a^'=( vec a+ vec b+ vec c)/([ vec a vec b vec c])` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

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

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 b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

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

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.

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

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

Prove that: ( vec a- vec b)*{( vec b- vec c)xx(vec c- vec a)}"=0

If veca , vec b and vec c represents three sides of a triangle taken in order prove that veca xx vec b = vec b xx vec c = vec c xx vec a

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

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. If vec a , vec b ,a n d vec c be three non-coplanar vector and p,q,...

    Text Solution

    |

  2. Find | -> a| and | -> b| , if ( -> a+ -> b)dot( -> a- -> b)=8 an...

    Text Solution

    |

  3. Let vec a , vec b ,a n d vec ca n d vec a^' , vec b^' , vec c ' are r...

    Text Solution

    |

  4. If vec a , vec b and vec c are three non-coplanar vectors, then ( v...

    Text Solution

    |

  5. Find the vector equation of the plane passing through the points havin...

    Text Solution

    |

  6. If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec...

    Text Solution

    |

  7. If vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec k a n d...

    Text Solution

    |

  8. If the vectors vec c , vec a=x hat i+y hat j+z hat k and vec b= hat j...

    Text Solution

    |

  9. Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx ve...

    Text Solution

    |

  10. If | vec a|=5,| vec a- vec b|=8 and | vec a+ vec b|=10 , then find | v...

    Text Solution

    |

  11. If A ,B ,C ,D are four distinct point in space such that vec(A B) is...

    Text Solution

    |

  12. If vec a=2 hat i+3 hat j-5 hat k , vec b=m hat i+n hat j+12 hat k and...

    Text Solution

    |

  13. If | vec a|=2| vec b|=5 and | vec axx vec b|=8, then find the value ...

    Text Solution

    |

  14. Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and inte...

    Text Solution

    |

  15. vec a , vec ba n d vec c are unit vectors such that | vec a+ vec b+3 v...

    Text Solution

    |

  16. Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, ve...

    Text Solution

    |

  17. Let A,B,C be three unit vectors and A.B= A.C=0. If the angel between ...

    Text Solution

    |

  18. The position vectors of the four angular points of a tetrahedron ar...

    Text Solution

    |

  19. If the vectors 2 hat i-3 hat j , hat i+ hat j- hat ka n d3 hat i- hat ...

    Text Solution

    |

  20. If vec u , vec v and vec w are three non-coplanar vectors, then pro...

    Text Solution

    |