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

  • #1

Homework Statement



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?


Homework Equations



->dl = dr ûr + r d∅ û∅ + dz ^k

->dl = dr ûr + r dθ ûθ + r sin (∅) û∅


The Attempt at a Solution

 

Answers and Replies

  • #2
SammyS
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Homework Statement



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?


Homework Equations



->dl = dr ûr + r d∅ û∅ + dz ^k

->dl = dr ûr + r dθ ûθ + r sin (∅) û∅


The Attempt at a Solution

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?
 
  • #3
Thanks, but can anyone provide me with a sample in sph.c. or cyl.c.?


Re: (2, π)
 
  • #4
SammyS
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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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