Home
Class 11
PHYSICS
If unit vectors hat(a) and hat(b) are in...

If unit vectors `hat(a)` and `hat(b)` are inclined at angle `theta`, then prove that
`|vec(a) - vec(b)| = 2 sin.(theta)/(2)`.

Promotional Banner

Topper's Solved these Questions

  • Motion in a Plane

    SL ARORA|Exercise Excercise|397 Videos

  • Motion in a Plane

    SL ARORA|Exercise Excercise|397 Videos

  • MECHANICS

    SL ARORA|Exercise Exercise|341 Videos

  • MOTION IN ONE DIMENSION

    SL ARORA|Exercise problems for self practice|66 Videos

Similar Questions

Explore conceptually related problems

Unit vector hat(P) and hat(Q) are inclined at an angle theta . Prove that |hat(P)-hat(Q)|= 2 sin(theta//2) .

If vec a and vec b are unit vectos inclined at an angle theta then the value of |vec a-vec b| is 2(sin theta)/(2) b.2sin theta c.2(cos theta)/(2) d.2 cos

If widehat a and hat b are unit vectors inclined at an angle theta, then prove that cos(theta)/(2)=(1)/(2)|widehat a+hat b|tan(theta)/(2)=(1)/(2)|(widehat a-hat b)/(widehat a+hat b)|

If widehat aandhat b are unit vectors inclined at an angle theta, then prove that (sin theta)/(2)=(1)/(2)|widehat a-hat b|

If widehat a and hat b are two unit vectors inclined at an angle theta, then sin((theta)/(2))

If widehat a and hat b are unit vectors inclined at an angle theta then prove that (cos theta)/(2)=(1)/(2)|widehat a+hat b|(tan theta)/(2)=(|widehat a-hat b|)/(|widehat a+hat b|)

Unit vectors widehat a and hat b are inclined at an angle 2 theta and |widehat a-hat b|<11 l 0<=theta<=pi?, then theta may belong to

If vec a and vec b are unit vectors and theta is the angle between them,then prove that cos[(theta)/(2)]=(1)/(2)|vec a+vec b|

If vec(a) and vec(b) are unit vectors and theta is the angle between them, then what is sin^(2)((theta)/(2)) equal to?

If theta is th angel between the unit vectors a and b ,then prove that cos(theta)/(2)=(1)/(2)|vec a+vec b|sin(theta)/(2)=(1)/(2)|vec a-vec b|

SL ARORA-Motion in a Plane-Example
  1. If vector P, Q and R have magnitude 5,12,and 13 units and vec(P)+vec(Q...

    Text Solution

    |

  2. Determine the angles which the vector vec(A) = 5 hati + 0 hatj +5hat...

    Text Solution

    |

  3. If unit vectors hat(a) and hat(b) are inclined at angle theta, then pr...

    Text Solution

    |

  4. If vec(A) +vec(B) = vec(C) and A^(2) +B^(2) = C^(2), then prove that v...

    Text Solution

    |

  5. Motion in two dimensions, in a plane can be studied by expressing posi...

    Text Solution

    |

  6. Prove that the vectors vec(A) = 2hati - 3hatj - hatk and vec(B) =- 6 h...

    Text Solution

    |

  7. Calculate the area of a paralleleogram whose two adjacent sides are fo...

    Text Solution

    |

  8. If vec(A) and vec(B) denpte the sides of a parallelogram and its area ...

    Text Solution

    |

  9. The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and...

    Text Solution

    |

  10. Find a unit vector perpendicular to each one of the vectors vec(a) = 4...

    Text Solution

    |

  11. Determine the sine of the angle between the vectors ( 3 hat i+ 3hat j+...

    Text Solution

    |

  12. Show that (vec(A) - vec(B)) xx (vec(A) +vec(B)) = 2(vec(A) xx vec(B))

    Text Solution

    |

  13. For any three vectors vec(A), vec(B) and vec(C) prove that vec(A) x...

    Text Solution

    |

  14. For any to vectors vec A and vec B, prove that | vec A xx vec B|^2 ...

    Text Solution

    |

  15. Find vec(A).vec(B) if |vec(A)| = 2, |vec(B)| = 5 and |vec(A) xx vec(B)...

    Text Solution

    |

  16. Find the area of the rriangle formed by the tips of the vectors, ve...

    Text Solution

    |

  17. Find the magnitude and direction cosines of the torque about the point...

    Text Solution

    |

  18. Find the area of parallelogram whose diagonals are the vectors 3 hat i...

    Text Solution

    |

  19. In any triangle ABC, prove that a sin A-b sin B -=c sin (A-B).

    Text Solution

    |

  20. If vec a ,\ vec b ,\ vec c are three vectors such that vec adot...

    Text Solution

    |