Home
Class 12
MATHS
If (vec a)^2 =(vec b)^2, is it necessary...

If `(vec a)^2 =(vec b)^2`, is it necessary that `vec a= vec b` ?

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

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

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 + vec c then is it true that |vec a|= |vec b|+ |vec c| ? Justify your answer

If vec a,vec b,vec c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is pi/2, then

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 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 and vec b are two vectors such that |quad vec a + vec b|= |quad vec a| , then prove that 2 vec a+ vec b is perpendicular to the vector vec b .

If vec aa n d vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b]dot

Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- vec c=0. If the area of triangle formed by vectors vec a and vec b is A , then what is the value of 4A^2?

Prove that (vec a+vec b)* (vec a+ vec b)=|vec a|^2 +|vec b|^2, if and only if vec a,vec b are perpendicular.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the value of a for which the vector 3 hat i+ 2 hat j+ 9 hat k and...

    Text Solution

    |

  2. Find the value of a for which the vector 3 hat i+ 2 hat j+ 9 hat k and...

    Text Solution

    |

  3. If (vec a)^2 =(vec b)^2, is it necessary that vec a= vec b ?

    Text Solution

    |

  4. Find the angles which the vector 3 hat i- 6 hat j+ 2 hat k makes the c...

    Text Solution

    |

  5. If vec a and vec b are two vectors such that |quad vec a + vec b|= |qu...

    Text Solution

    |

  6. If vec a and vec b are two vectors such that |quad vec a + vec b|= |qu...

    Text Solution

    |

  7. If vec a is any vector in space, then show that vec a= ( vec a* hat i...

    Text Solution

    |

  8. If the vertices A,B,C of triangle ABC have position vectors (1,2,3), (...

    Text Solution

    |

  9. If hat i+ hat j+ hat k,2 hat i+ 5 hat j, 3 hat i+ 2 hat j- 3 hat k and...

    Text Solution

    |

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

    Text Solution

    |

  11. Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on ...

    Text Solution

    |

  12. Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on ...

    Text Solution

    |

  13. Find the projection of vec AB on vec PQ where P,Q,A,B are the points (...

    Text Solution

    |

  14. If A,B,C,D are the points with position vectors hat i+ hat j-hat k, 2 ...

    Text Solution

    |

  15. Find the projection of the vector vec a = 2 hat i+ 3 hat j+ 2 hat k on...

    Text Solution

    |

  16. Find the projection of thevector hat i+ 3 hat j+ 7 hat k on the vector...

    Text Solution

    |

  17. Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat ...

    Text Solution

    |

  18. If A,B,C have position vectors (0,1,1),(3,1,5),(0,3,3) respectively, p...

    Text Solution

    |

  19. Prove Cauchy- Schwarz inequality |quad vec a* vec b|<|quad vec a||quad...

    Text Solution

    |

  20. For any two vectors vec a and vec b, prove that (vec a* vec b)^ 2 le |...

    Text Solution

    |