# Spherical coordinates

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1. Mar 26, 2016

### Dong Hoon Lee

1. The problem statement, all variables and given/known data
transform the following vectors to spherical coordinates at the points given

10ax at P (x = -3 , y = 2, z=4)

2. Relevant equations
x y z can be chage into x = rsinθcosφ , y=rsinθsinφ , z=cosθ

3. The attempt at a solution
ax vector can be expressed ar,aθ,aφ so, I can change x , y, z through 2.

therefore we have to find θ, φ, r

also, we can know the sinθcosφ = x/r sinθsinφ = y/r z=cosθ

10ax = 10ax ar + 10ax aθ + 10ax aφ

= 10sinθcosφ + 10cosθcosφ - 10sinφ

>>>> I can fill out innerproduct between x and r but how to solve the others,

Is it right answer? I want to find more correctly one (it make lots of number, because find each variables through lots of calculation)

>>>> I want to more objective soultion !

>>>>> want to know how to chage between sehperical coordinates and cartesian coordinates

Thank you for your attention for me

2. Mar 26, 2016

### Simon Bridge

You have three equations and three unknowns.
It is better to use geometry though ... ferinstance "r" is the magnitude of the vector $\vec r$, which is given by $r^2=x^2+y^2+z^2$
Try sketching the vector.

I notice that "10ax" is not a vector though.

3. Mar 27, 2016

### Simon Bridge

Of course you could always just look up the transformation from cartesian to spherical ...

4. Mar 27, 2016

### Ray Vickson

When you write $10ax$ do you really mean $10 a \vec{r} = 10 a \langle x,y,z \rangle?$ One of these is a vector and the other is not.

5. Mar 28, 2016

### Simon Bridge

Hmmm ... looking at the later notation: OP may be using "a" to indicate the unit vector ... see ar aφ etc later on, as in
So 10ax would mean $\vec r = 10\hat a_x = (10,0,0)$ cartesian ... which is very easy to put in spherical coordinates.
OTOH: that does not fit so well with the rest of the problem statement: the vector does not depend on position for example.

OP has been back since I replied and "liked" the reply ... presumably got what was needed.