# Spherical coordinates vector

1. Oct 5, 2015

### azizlwl

1. The problem statement, all variables and given/known data
Find the vector directed from (10,3π/4,π/6) to (5, π/4,π), where the endpoints are given in spherical
coordinates. Ans -9.660ax, - 3ay. + 10.61az

2. Relevant equations
az=rCosΦ

3. The attempt at a solution
az=10Cos(π/6) +5Cos(π) =13.6

My answer differs. Where did i go wrong?

2. Oct 5, 2015

### BvU

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

3. Oct 5, 2015

### azizlwl

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

4. Oct 5, 2015

### BvU

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

5. Oct 5, 2015

### 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)

6. Oct 5, 2015

### 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 !

7. Oct 5, 2015

### BvU

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

8. Oct 5, 2015

### azizlwl

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

9. Oct 5, 2015

### Ray Vickson

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?

Last edited: Oct 5, 2015