Transform Vectors to Spherical Coordinates at P (-3,2,4)

AI Thread Summary
The discussion focuses on transforming vectors to spherical coordinates at the point P (-3, 2, 4). The user outlines the relationships between Cartesian coordinates (x, y, z) and spherical coordinates (r, θ, φ), expressing the need to find these angles and the radius. They attempt to convert the vector 10ax into spherical components but seek clarification on the calculations and the correct approach. Additionally, the user expresses a desire for a more objective solution and inquires about deleting their post. The conversation highlights the complexities of coordinate transformation and the need for precise mathematical methods.
Dong Hoon Lee
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The problem is

<< transform the following vectors to spherical coordinates at the points given

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

Actually, My first language isn't English, please understand that.

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


ax vector can be expressed ar,aθ,aφ so, I can change x , y, z

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 !
 
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I want to know how to chage between sehperical coordinates and cartesian coordinates
 
I am sorry that I posted wrong forum,,, how can i erase my post?
 

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