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

If ` vec a , vec b , vec ca n d vec d` are the position vectors of the vertices of a cyclic quadrilateral `A B C D ,` prove that `(| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/((vec b- vec a).(vec d- vec a)) + (| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/((vec b- vec c).( vec d- vec c))=0dot`

Promotional Banner

Topper's Solved these Questions

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

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= a. 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= a. [ vec a\ vec b\ vec c] b. 0 c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

If vec a , vec b ,a n d vec c are three non-coplanar vectors, then find the value of ( vec a .( vec bxx vec c))/( vec b .( vec cxx vec a))+( vec b .( vec cxx vec a))/( vec c .( vec axx vec b))+( vec c . ( vec bxx vec a))/( vec a . ( vec bxx vec c))

Prove that : vec(a) . { vec(b) xx (vec(c) + vec(d))} = vec(a) . (vec(b)xx vec(c)) + vec(a) . ( vec(b) xx vec(d))

If vec axx vec b= vec cxxvec d and vec axxvec c= vec bxxvec d, vec a ne vec d, vec b ne vec c then show that vec b- vec c is parallel to vec a-vec d

For any four vectors, vec a , vec b , vec c and vec d prove that vec d.( vec axx( vec bxx( vec cxx vec d)))=( vec b. vec d)[ vec a \ vec c \ vec d] .

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

Let vec(a),vec(b),vec (c ) be the positions vectors of the vertices of a triangle , prove that the area of the triangle is 1/2| vec(a) xx vec(b) + vec(b) xx vec(c)+ vec(c)xx vec(a)|

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. Let vec a=x hat i+12 hat j- hat k , vec b=2 hat i+2x hat j+ hat ka n ...

    Text Solution

    |

  2. If vec a , vec b ,a n d vec c are three non-coplanar vectors, then ...

    Text Solution

    |

  3. If vec a , vec b , vec ca n d vec d are the position vectors of the...

    Text Solution

    |

  4. The position vectors of the vertices of a quadrilateral with A as o...

    Text Solution

    |

  5. If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , t...

    Text Solution

    |

  6. Show by a numerical example and geometrically also that vec axx ve...

    Text Solution

    |

  7. In triangle A B C ,points D , Ea n dF are taken on the sides B C ,C Aa...

    Text Solution

    |

  8. Let A ,B ,C be points with position vectors 2 hat i- hat j+ hat k , ...

    Text Solution

    |

  9. Let vec a and vec b be unit vectors such that | vec a+ vec b|=sqrt(3)...

    Text Solution

    |

  10. If u and v are two non-collinear unit vectors such that |vecu...

    Text Solution

    |

  11. A rigid body is spinning about a fixed point (3,-2,-1) with an angu...

    Text Solution

    |

  12. vec rxx vec a= vec bxx vec a ; vec rxx vec b= vec axx vec b ; vec a!= ...

    Text Solution

    |

  13. If | vec a|=2, then find the value of | vec axx hat i|^2+| vec axx hat...

    Text Solution

    |

  14. If veca , vecb , vecc are position vectors of the vertices A, ...

    Text Solution

    |

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

    Text Solution

    |

  16. Find the area of the parallelogram whose adjacent sides are determin...

    Text Solution

    |

  17. Using vectors, find the area of the triangle with vertices A (1, 1,...

    Text Solution

    |

  18. Let vec a , vec ba n d vec c be three verctors such that vec a!=0...

    Text Solution

    |

  19. Find the area of a parallelogram whose diagonals are vec a=3 hat i+...

    Text Solution

    |

  20. If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 ve...

    Text Solution

    |