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 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

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

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

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] .

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

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

Prove that [ vec a , vec b , vec c+ vec d]=[ vec a , vec b , vec c]+[ vec a , vec b , vec d]

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lam...

    Text Solution

    |

  2. If a \ a n d \ c are unit vectors and |b|=4 . The angel between aa n d...

    Text Solution

    |

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

    Text Solution

    |

  4. Let vec a , vec b , a n d vec c be three non-coplanar vectors and ...

    Text Solution

    |

  5. If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec ...

    Text Solution

    |

  6. If vec a \ a n d \ vec b are two non-collinear unit vector, and ...

    Text Solution

    |

  7. The angles of triangle, two of whose sides are represented by vector...

    Text Solution

    |

  8. vec a , vec b ,a n d vec c are unimodular and coplanar. A unit vector...

    Text Solution

    |

  9. Vectors perpendicular to hat i- hat j- hat k and in the plane of hat...

    Text Solution

    |

  10. If side vec A B of an equilateral trangle A B C lying in the x-y plan...

    Text Solution

    |

  11. 36. If vec a, vec b,vec c and vec d are unit vectors such that (vec a ...

    Text Solution

    |

  12. Let two non-collinear unit vector hat a a n d hat b form an acute a...

    Text Solution

    |

  13. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

    Text Solution

    |

  14. If vec a , vec b and vec c are three non-zero, non coplanar vecto...

    Text Solution

    |

  15. The unit vector which is orthogonal to the vector 3 hat j+2 hat j+6 ...

    Text Solution

    |

  16. If vec a and vec b are unequal unit vectors such that ( vec a- vec ...

    Text Solution

    |

  17. If veca,vecb,vecc are 3 unit vectors such that vecaxx(vecbxxvecc)=vec...

    Text Solution

    |

  18. If in triangle A B C , vec A B= vec u/(| vec u|)- vec v/(| vec v|)a n ...

    Text Solution

    |

  19. A vector vec d is equally inclined to three vectors vec a= hat i+ ...

    Text Solution

    |

  20. If axx(bxxc)=(axxb)xxc , then ( vec cxx vec a)xx vec b= vec0 b. vec cx...

    Text Solution

    |