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

[Tanegashima]

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

 

[SammyS]

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?

 

[Tanegashima]

Thanks, but can anyone provide me with a sample in sph.c. or cyl.c.?Re: (2, π)

 

[SammyS]

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.