Home
Class 12
MATHS
If vec a,vec b,vec c are coplanar vector...

If `vec a`,`vec b`,`vec c` are coplanar vectors, prove that `|[vec a, vec b, vec c],[vec a.vec a ,vec a.vec b,vec a.vec c],[vec b.vec a, vec b.vec b, vec b.vec c]|=vec 0`.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    PRADEEP PUBLICATION|Exercise EXERCISE|438 Videos

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

Similar Questions

Explore conceptually related problems

Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

If vec a,vec b,vec c are any three vectors, prove that vec a xx (vec b xx vec c) +vec b xx(vec c xx vec a)+ vec c xx(vec a xx vec b) = vec 0

If vec a and vec b are any two vectors, show that |vec a xxvec b|^2= [[vec a*vec a,vec a*vec b],[vec a*vec b,vec b* vec b]] .

If vec a , vec b , vec c are vectors such that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c , vec a!= vec0, then show that vec b= vec c

If vec a,vec b,vec c are unit vectors such that vec a+vec b+ vec c= vec 0 , then the value of vec a *vec b +vec b* vec c+ vec c*vec a is equal to

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c = vec 0 , then find the value of vec a* vecb + vec b* vec c +vec c* veca .

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| .

For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ , vec b+ vec c\ , vec c+ vec a]=2\ [ vec a\ vec b\ vec c]dot

Prove that if vec a,vec b,vec c and vec d are any four vectors, then (vec a xx vec b)*(vec c xx vec d)= [[vec a* vec c vec b* vec c], [vec a* vec d vec b* vec d]]

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If vec a,vec b,vec c are coplanar vectors, prove that |[vec a, vec b, ...

    Text Solution

    |

  2. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  3. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  4. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  5. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  6. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  7. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  8. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  9. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  10. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  11. Find lambda in R such that |quad lambda vec a|=1, vec a being a non-ze...

    Text Solution

    |

  12. If |quad vec a|=2, find |quad 4 vec a |, |10 vec a| and |(-5 ) vec a |...

    Text Solution

    |

  13. Is it possible that |quad vec a+ vec b|= |quad vec a|+ |quad vec b|? I...

    Text Solution

    |

  14. If vec a = vec b, is it true that |quad vec a|=|quad vec b| ?

    Text Solution

    |

  15. Does |quad vec a|= |quad vec b| imply vec a= vec b?

    Text Solution

    |

  16. If A,B,C,D are the points with position vectors vec a,vec b, 3 vec a+ ...

    Text Solution

    |

  17. If vec c= 3 vec a + 4 vec b and 2 vec c = vec a- 3 vec b, show that ve...

    Text Solution

    |

  18. If the position vector of a point A is vec a + 2 vec b and vec a divi...

    Text Solution

    |

  19. If ABC is triangle and D is the mid-point of [BC], prove that vec AB +...

    Text Solution

    |

  20. If vec a = hat i + hat j+ 2hat k and vec b =2 hat i+ hat j - 2 hat k, ...

    Text Solution

    |

  21. If vec a = 5hat i - hat j- 2hat k and vec b =5 hat i+ hat j - 2 hat k,...

    Text Solution

    |