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

    MODERN PUBLICATION|Exercise Exercise|500 Videos

  • UNIT TEST-4

    MODERN PUBLICATION|Exercise EXERCISE|13 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

MODERN PUBLICATION-VECTORS-Exercise
  1. Find a unit vector perpendicular to each of the vectors (veca+vecb) an...

    Text Solution

    |

  2. Find a vector of magnitude 9, which is perpendicular to both the vecto...

    Text Solution

    |

  3. If vec a and vec b are unit vectors and theta is the angle between the...

    Text Solution

    |

  4. Determine the area of the parallelogram whose adjacent sides are 2 hat...

    Text Solution

    |

  5. determine the area of the parallelogram whose adjacent sides are : 2ha...

    Text Solution

    |

  6. Find the area of a parallelogram whose adjacent sides are : 3hati+ha...

    Text Solution

    |

  7. determine the area of the parallelogram whose adjacent sides are : hat...

    Text Solution

    |

  8. determine the area of the parallelogram whose adjacent sides are : hat...

    Text Solution

    |

  9. Find the area of the parallelogram whose diagonals are : veca=hati-2ha...

    Text Solution

    |

  10. Find the area of the quadrilateral whose diagonals are given by 3hat...

    Text Solution

    |

  11. Show that the area of the parallelogram with diagonals veca and vecb, ...

    Text Solution

    |

  12. Show that |vecaxxvecb|=sqrt(vec(a^2)vec(b^2)-(veca*vecb)^2).

    Text Solution

    |

  13. Prove that |vecaxxvecb|/(veca*vecb)= tan theta, where theta is the ang...

    Text Solution

    |

  14. Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb).

    Text Solution

    |

  15. Given that veca cdot vecb = 0 and vecaxxvecb = vec0. What can you conc...

    Text Solution

    |

  16. Find |veca*vecb|, if |veca|=5,|vecb|=13 and |vecaxxvecb|=25.

    Text Solution

    |

  17. If |veca|=13,|vecb|=5 and veca*vecb=60, then find |vecaxxvecb|.

    Text Solution

    |

  18. Find lambda and mu if : (2hati+6hatj+27hatk)xx(hati+lambdahatj+muhatk)...

    Text Solution

    |

  19. If veca=2hati+sqrt3hatj+3hatk and vecb=3hati+2hatj-2sqrt3hatk, then : ...

    Text Solution

    |

  20. If veca=2hati+sqrt3hatj+3hatk and vecb=3hati+2hatj-2sqrt3hatk, then : ...

    Text Solution

    |