Home
Class 12
MATHS
If vec d= vec axx vec b+ vec bxx vec c+...

If ` vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a` is non-zero vector and `|( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0,` then
a.`| vec a|=| vec b|=| vec c|`
b. `| vec a|+| vec b|+| vec c|=|d|`
c. ` vec a , vec b ,a n d vec c` are coplanar
d. none of these

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

If vec a , vec b , and vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c| .

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

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

If vec a= vec b+ vec c , vec b X vecd= vec0 and vec c*vec d=0 then ( vec dx( vec ax vec d))/( vec d^2) is equal to (a) vec a (b) vec b (c) vec c (d) vec d

The lines vec r= vec a+lambda( vec bxx vec c)a n d vec r= vec b+mu( vec cxx vec a) will intersect if a. vec axx vec c= vec bxx vec c b. vec adot vec c= vec bdot vec c c. bxx vec a= vec cxx vec a d. none of these

If axx(bxxc)=(axxb)xxc , then ( vec cxx vec a)xx vec b= vec0 b. vec cxx( vec axx vec b)= vec0 c. vec bxx( vec cxx vec a) =0 d. ( vec cxx vec a)xx vec b= vec bxx( vec cxx vec a)= vec0

For any three vectors veca , vec b , vec c show that vecaxx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)= vec0

( 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]

[( 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]

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

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. If vec a=2 hat i+ hat j+ hat k , vec b= hat i+2 hat j+2 hat k , vec c...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If vece(1),vece(2),vece(3)and vecE(1),vecE(2),vecE(3) arwe two sets of...

    Text Solution

    |

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

    Text Solution

    |

  15. Given the vectors vec A , vec B ,a n d vec C form a triangle such tha...

    Text Solution

    |

  16. If vec a , vec ba n d vec c are three mutually perpendicular vecto...

    Text Solution

    |

  17. Let a three dimensional vector vec V satisfy the condition, 2 vec ...

    Text Solution

    |

  18. If vec a=3 hat i- hat j-4 hat k , vec b=2 hat i+4 hat j-3 hat k and ...

    Text Solution

    |

  19. Let vec O A= vec a , hat O B=10 vec a+2 vec ba n d vec O C= vec b ,w ...

    Text Solution

    |

  20. If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= ...

    Text Solution

    |