Calculate the distance between these two points (sphr. and cyl. coordinates)

  1. 1. The problem statement, all variables and given/known data

    Calculate the distance between these two points:

    (3;π/2;−1) and (5;3π/2;5) (cylindrical coordinates)
    (10;π/4;3π/4) and (5;π/6;7π/4) (spherical coordinates)


    Do I need to put them in cartesian coordinates and continue the calc. or can I do with integrals?


    2. Relevant equations

    ->dl = dr ûr + r d∅ û∅ + dz ^k

    ->dl = dr ûr + r dθ ûθ + r sin (∅) û∅


    3. The attempt at a solution
     
  2. jcsd
  3. SammyS

    SammyS 8,882
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    Hi Tanegashima. Welcome to PF.

    It's likely easier in Cartesian coordinates . But for the first one, what is the distance from (3, π/2) to (5, 3π/2) in polar coordinates?
     
  4. Thanks, but can anyone provide me with a sample in sph.c. or cyl.c.?


    Re: (2, π)
     
  5. SammyS

    SammyS 8,882
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    No. The distance from (3, π/2) to (5, 3π/2) is 8.

    Therefore, the distance (horizontal) from (3, π/2, -1) to (5, 3π/2, -1) is 8 units.

    Of course the distance from (5, 3π/2, -1) to (5, 3π/2, 5) is 6 units.

    These two distances are perpendicular to each other.
     
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