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

    Text Solution

    |

  2. Let vec pa n d vec q be any two orthogonal vectors of equal magnitu...

    Text Solution

    |

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

    Text Solution

    |

  4. Find a unit vector perpendicular to each of the vectors ( vec a+ vec...

    Text Solution

    |

  5. Consider three vectors vec a , vec b and vec c Statement 1 vec axx...

    Text Solution

    |

  6. Column I, Column II The possible value of vec a if vec r=( hat i+ ha...

    Text Solution

    |

  7. If vec A, vec B and vec C are vectors such that |vec B|-|vec C|. Prove...

    Text Solution

    |

  8. A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b...

    Text Solution

    |

  9. Statement 1: Vector vec c=-5 hat i+7 hat j+2 hat k is along the bisec...

    Text Solution

    |

  10. Statement 1: A component of vector vec b=4 hat i+2 hat j+3 hat k in...

    Text Solution

    |

  11. Statement 1 : Points A(1,0),B(2,3),C(5,3),a n dD(6,0) are concyclic. S...

    Text Solution

    |

  12. Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdo...

    Text Solution

    |

  13. Let vec a = a1 hat i + a2 hat j+ a3 hat k;vec b = b1 hat i+ b2 hat j+...

    Text Solution

    |

  14. Statement-I A=2hat(i)+3hat(j)+6hat(k), B=hat(i)+hat(j)-2hat(k) and C=h...

    Text Solution

    |

  15. If vec a\ a n d\ vec b\ a n d\ vec c are mutually perpendicular uni...

    Text Solution

    |

  16. Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec ax...

    Text Solution

    |

  17. The number of vectors of unit length perpendicular to vectors vec ...

    Text Solution

    |

  18. For any two vec aa n d vec b ,( vec axx hat i).( vec bxx hat i)+( vec...

    Text Solution

    |

  19. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

    Text Solution

    |

  20. If vec a is parallel to vec bxx vec c , then ( vec axx vec b)dot( ve...

    Text Solution

    |