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

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 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)

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Find the shortest distance between the following pair of lines and ...

    Text Solution

    |

  2. 5 Indian & 5 American couples meet at a party& shake hands. If no wife...

    Text Solution

    |

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

    Text Solution

    |

  4. A bag initially contains 1 red and 2 blue balls. An experiment consist...

    Text Solution

    |

  5. In a A B C , if A B=5c m ,B C=13a n dC A=12 c m , then the distance o...

    Text Solution

    |

  6. Projection of line (x+1)/2+(y+1)/(-1)=(z+3)/4 on the plane x+2y+z=6; h...

    Text Solution

    |

  7. The number of times the digit 3 will be written when listing the integ...

    Text Solution

    |

  8. A writes a letter to his friend B and gives it to his son to post i...

    Text Solution

    |

  9. If (1+x+x^2++x^p)^n=a0+a1x+a2x^2++a(n p)x^(n p), then find the value o...

    Text Solution

    |

  10. Let A and B be two independent even such that P(A)=1/3 " and " P(B)=1/...

    Text Solution

    |

  11. If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the su of C1+2C3+3C...

    Text Solution

    |

  12. A six-faced dice is so biased that it is twice as likely to show an ev...

    Text Solution

    |

  13. If the difference between mean and m0de is 63, the difference between ...

    Text Solution

    |

  14. If 60% of\ A=3/4of\ B ,\ t h e n\ A : B is 4:5 b. 5:4 c. 9: 20 d. 20 :...

    Text Solution

    |

  15. The product of the arithmetic mean of the lengths of the sides of a ...

    Text Solution

    |

  16. For finding average speed of a vehicle covering equal distances in d...

    Text Solution

    |

  17. Internal bisector of angle A of Delta ABC meets side BC to D. A line ...

    Text Solution

    |

  18. Statement 1: Sum of squares of deviations is minimum when it is take...

    Text Solution

    |

  19. In the Mean value theorem f(b)-f(a)=(b-a)f'(c), if a=4, b=9 and f(...

    Text Solution

    |

  20. In a triangle A B C , if a : b : c=3:7:8,t h e n R : r is equal to a. ...

    Text Solution

    |