Home
Class 12
MATHS
Let vec a , vec ba n d vec c be three n...

Let ` vec a , vec ba n d vec c` be three non-coplanar vecrors and ` vec r` be any arbitrary vector. Then `( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b)` is always equal to `[ vec a vec b vec c] vec r` b. `2[ vec a vec b vec c] vec r` c. `3[ vec a vec b vec c] vec r` d. none of these

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

( vec a+2 vec b- vec c)dot{( vec a- vec b)xx( vec a- vec b- vec c)} is equal to [ vec a\ vec b\ vec c] b. c. 2[ vec a\ vec b\ vec c] d. 3[ vec a\ vec b\ vec c]

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)

For any three vectors vec a ,\ vec b ,\ vec c the expression ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)} equals [ vec a\ vec b\ vec c] b. "\ "2[ vec a\ vec b\ vec c]"\ " c. [ vec a\ vec b\ vec c]^2 d. none of these

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

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

( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= [ 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 and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

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

If vec a,vec b,vec c are three non-coplanar vectors represented by concurrent edges of a parallelopiped of volume 4, (vec a+vec b)+(vec bxx vec c)+(vec b+vec c).(vec c xx vec a) + (vec c +vec a).(vec axx vec b) is equal to

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

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. [( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)(...

    Text Solution

    |

  2. If V be the volume of a tetrahedron and V ' be the volume of another...

    Text Solution

    |

  3. Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...

    Text Solution

    |

  4. A(veca),B(vecb),C(vecc) are the vertices of the triangle ABC and R(vec...

    Text Solution

    |

  5. Let vec a , vec ba n d vec c be three non-coplanar vectors and v...

    Text Solution

    |

  6. Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...

    Text Solution

    |

  7. The position vectors of point A ,B ,a n dC are hat i+ hat j+ hat k...

    Text Solution

    |

  8. Let vec a(x)=(sin x) hat i+(cosx) hat j a n d vec b(x)=(cos2x) hat i+...

    Text Solution

    |

  9. If vec a=2 hat i+ hat j+ hat k , vec b= hat i+2 hat j+2 hat k , vec c...

    Text Solution

    |

  10. If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...

    Text Solution

    |

  11. If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vec...

    Text Solution

    |

  12. The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...

    Text Solution

    |

  13. Let vec a=- hat i- hat k , vec b=- hat i+ hat ja n d vec c= hat i+2 h...

    Text Solution

    |

  14. Let vec a , vec b ,a n d vec c be vectors forming right-hand traid. L...

    Text Solution

    |

  15. From a point O inside a triangle A B C , perpendiculars O D ,O Ea n dO...

    Text Solution

    |

  16. Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i...

    Text Solution

    |

  17. Find the work done by the force F=3 hat i- hat j-2 hat k acrting on ...

    Text Solution

    |

  18. Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=...

    Text Solution

    |

  19. O A B C is regular tetrahedron in which D is the circumcentre of O...

    Text Solution

    |

  20. In the quadrilateral ABCD, the diagonals AC and BD are equal and perpe...

    Text Solution

    |