How to find the vector between two points given in spherical coordinates?

[azizlwl]

Homework Statement

Find the vector directed from (10,3π/4,π/6) to (5, π/4,π), where the endpoints are given in spherical
coordinates. Ans -9.660a_x, - 3a_y. + 10.61a_z

Homework Equations

a_z=rCosΦ

The Attempt at a Solution

a_z=10Cos(π/6) +5Cos(π) =13.6

My answer differs. Where did i go wrong?

 

[BvU]

Nice answer, but: how did you get it ? Please show the detailed steps you take.

 

[azizlwl]

Nice answer, but: how did you get it ? Please show the detailed steps you take.

I'm not sure which answer you refer to. The answer is given in the book. I did only for z-axis in Cartesians coordinates. The answer from the book foe z-axis is 10.61 but my calculation, az=10Cos(π/6) +5Cos(π) =13.6

 

[BvU]

I'm not sure which answer you refer to

the only answer I see is the a_z. What did you do to get it ? (It looks to me you are adding z-coordinates)

 

[azizlwl]

Spherical coordinates
A= (10,3π/4,π/6)
B= (5, π/4,π),

X=rSinΦCosθ
Y=rSinΦSinθ
Z=rCosΦ
Cartesian coordinates
A=(-3.53, 3.53, 8.66)
B=(0 ,0, -5)

AB= B-A=(3.53, -3.53, -13.66)

 

[BvU]

Ah, I see. Not only the z coordinate answer differs !

You assume you are given $(r, \phi, \theta)$. The "usual" order may well be $(r, \theta, \phi)$. Eureka !

 

[BvU]

Turns out here is a set of two pictures that might explain why you and the book perceived differently !

 

[azizlwl]

Ah, I see. Not only the z coordinate answer differs !

You assume you are given $(r, \phi, \theta)$. The "usual" order may well be $(r, \theta, \phi)$. Eureka !

Thank you. Get the answer and know where's the error.

 

[Ray Vickson]

Homework Statement

Find the vector directed from (10,3π/4,π/6) to (5, π/4,π), where the endpoints are given in spherical
coordinates. Ans -9.660a_x, - 3a_y. + 10.61a_z

Homework Equations

a_z=rCosΦ

The Attempt at a Solution

a_z=10Cos(π/6) +5Cos(π) =13.6

My answer differs. Where did i go wrong?

Be careful: there are two common versions of spherical coordinates: see, eg., https://en.wikipedia.org/wiki/Spherical_coordinate_system . Which convention does your problem use?

Note added in edit: again, many of the replies did not appear on my screen until after I posted the current message. Posts # 6,7,8 were unavailable to me until after I hit the "enter" key. That keeps happening. Does anyone know why?