How to Convert Vectors to Spherical Coordinates at Given Points?

[Dong Hoon Lee]

Homework Statement

transform the following vectors to spherical coordinates at the points given

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

Homework Equations

x y z can be chage into x = rsinθcosφ , y=rsinθsinφ , z=cosθ

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

 

[Simon Bridge]

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

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.

 

[Simon Bridge]

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

 

[Ray Vickson]

Homework Statement

transform the following vectors to spherical coordinates at the points given

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

Homework Equations

x y z can be chage into x = rsinθcosφ , y=rsinθsinφ , z=cosθ

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

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.

 

[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

10ax = 10ax ar + 10ax aθ + 10ax aφ

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.