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.