Home
Class 12
MATHS
If vec adot vec a=0\ a n d\ vec adot v...

If ` vec adot vec a=0\ a n d\ vec adot vec b=0\ ` what casn you conclude about the vector ` vec b ?`

Text Solution

Verified by Experts

It is given that `veca.veca = 0` or `|veca|^2=0`
`⇒|veca|=0`
`⇒veca=0`
i.e., `veca` is a zero vector because its magnitude is zero.
Hence, `veca.vecb = 0 ` whatever `vecb` may br (`∵veca = 0`).
This means that nothing can be concluded about `vecb`, it can be any vector.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|197 Videos

  • SCALAR TRIPLE PRODUCT

    RD SHARMA|Exercise Solved Examples And Exercises|59 Videos

Similar Questions

Explore conceptually related problems

If vec adot a=0 and vec avec b=0 what can you conclude about the vector vec b?

If vec a*vec a=0 and vec a*vec b=0, what can you conclude about the vector vec b?

If vec a*vec a=0 and vec a*vec b=0, then what can be concluded about the vector vec b?

Given that vec avec b=0 and vec a xxvec b=0. What can you conclude about the vectors vec a and vec b

If | vec a|=10 ,\ | vec b|=2\ a n d\ | vec axx vec b|=16 find vec adot vec bdot

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is vec bdot vec c= vec adot vec d b. vec adot vec b= vec cdot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec cdot vec d=0

If | vec a|=2,| vec b|=5a n d vec adot vec b=0, then vec ax( vec ax( vec ax( vec ax( vec a x( vec ax vec b))))) is equal to 64 vec a (b) 64 vec b (c) -64 vec b (d) -64 vec a

If vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k , then find the vaue of | vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec a vec bdot vec a vec cdot vec a vec cdot vec a vec cdot vec a| .

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

RD SHARMA-SCALAR OR DOT PRODUCT-Solved Examples And Exercises
  1. Decompose the vector 6 hat i-3 hat j-6 hat k into vectors which are pa...

    Text Solution

    |

  2. Let vec a=5 hat i- hat j+7 hat k\ a n d\ vec b= hat i- hat j+lambda ...

    Text Solution

    |

  3. If vec adot vec a=0\ a n d\ vec adot vec b=0\ what casn you conclud...

    Text Solution

    |

  4. If vec c is perpendicular to both vec a\ a n d\ vec b , then prove ...

    Text Solution

    |

  5. If | vec a|= a\ a n d\ | vec b|=b, prove that ( vec a/(a^2)- vec b/(b^...

    Text Solution

    |

  6. If vec a ,\ vec b ,\ vec c are three non coplanar vectors such that...

    Text Solution

    |

  7. If a vector vec a is perpendicular to two non collinear vectors vec ...

    Text Solution

    |

  8. If vec a+ vec b+ vec c= vec0, show that the angle theta between the v...

    Text Solution

    |

  9. Let vec u ,\ vec v\ a n d\ vec w be vector such vec u+ vec v+ vec ...

    Text Solution

    |

  10. Let vec a=x^2 hat i+2 hat j-2 hat k ,\ vec b= hat i- hat j+ hat k\ a...

    Text Solution

    |

  11. Find the value of x\ a n d\ y if the vectors vec a=3 hat i+x hat j- h...

    Text Solution

    |

  12. If vec a\ a n d\ vec b are two non collinear unit vectors such that...

    Text Solution

    |

  13. If vec a ,\ vec b are two vectors such that | vec a+ vec b|\ =| vec ...

    Text Solution

    |

  14. Prove using vectors: The median to the base of an isosceles triangl...

    Text Solution

    |

  15. Show that the diagonals of a rhombus bisect each other at right ang...

    Text Solution

    |

  16. Using vector method, prove that the angel in a semi circle is a rig...

    Text Solution

    |

  17. Prove that the cosine formula for triangles is equivalent to the de...

    Text Solution

    |

  18. In a triangle O A B ,\ /A O B=90^0dot If P\ a n d\ Q are points of tri...

    Text Solution

    |

  19. Prove that the if the diagonals of a quadrilateral bisect each othe...

    Text Solution

    |

  20. (Pythagoras’s Theorem) Prove by vector method that in a right angle...

    Text Solution

    |