Home
Class 12
MATHS
If vec a and vec b are unit vectors and ...

If `vec a` and `vec b` are unit vectors and `theta` is the angle between them, show that `(sin theta/2=1/2|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

Let vec a and vec b be two unit vectors and θ is the angle between them. Then vec a+vec b is a unit vector if

If vec a and vec b are non-zero vectors and the angle θ between them is given by cos θ= k/(|vec a||vec b|) then write the value of k.

If |vec a|=10, and |vec b|=2 and vec a* vec b =12 , find angle between the two vectors

If vec a , vec b are any two vectors, then give the geometrical interpretation of relation | vec a+ vec b|=| vec a- vec b|

If vec a, vec b and sqrt(3)veca-vec b are Unit Vectors, then the angle between vec a and vec b is .........

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 a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot

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 mutually perpendicular vectors of equal magnitudes, then find the angle between vectors vec a and vec a+ vec b+ vec c dot

If vec a , vec b , vec c are unit vectors such that vec adot vec b=0= vec adot vec c and the angle between vec ba n d vec c is pi//3 , then the value of | vec axx vec b- vec axx vec c| is 1//2 b. 1 c. 2 d. none of these

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If vec a and vec b are unit vectors and theta is the angle between the...

    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

    |