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

Click For Summary
SUMMARY

The discussion focuses on transforming vectors from Cartesian coordinates to spherical coordinates at the point P (-3, 2, 4). The transformation equations used are x = r sinθ cosφ, y = r sinθ sinφ, and z = r cosθ. The user seeks clarification on calculating the angles θ and φ, as well as the radius r, while expressing the vector 10ax in terms of spherical components. The conversation highlights the need for a more objective solution to the conversion process and the user's desire to correct their forum post.

PREREQUISITES
  • Understanding of spherical coordinates and their relationship to Cartesian coordinates
  • Familiarity with vector notation and operations in three-dimensional space
  • Knowledge of trigonometric functions and their applications in coordinate transformations
  • Basic proficiency in mathematical problem-solving and algebra
NEXT STEPS
  • Study the derivation of spherical coordinate transformations from Cartesian coordinates
  • Learn how to calculate angles θ and φ using inverse trigonometric functions
  • Explore vector decomposition in spherical coordinates and its applications
  • Practice converting between Cartesian and spherical coordinates with various examples
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who need to understand vector transformations and coordinate systems in three-dimensional space.

Dong Hoon Lee
Messages
4
Reaction score
0
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 !
 
Engineering news on Phys.org
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?
 

Similar threads

How to Convert Vectors to Spherical Coordinates at Given Points?
  • · Replies 4 ·
Replies
4
Views
6K
High School Method of images and spherical coordinates
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Transforming coordinates between Cartesian and spherical
  • · Replies 1 ·
Replies
1
Views
3K
How to calculate a sink using spherical coordinates
  • · Replies 7 ·
Replies
7
Views
1K
Deriving the Laplacian in spherical coordinates
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Dot product in spherical coordinates
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Velocity Vector Transformation from Cartesian to Spherical Coordinates
  • · Replies 2 ·
Replies
2
Views
4K
Convert unit vector from cartesian to spherical coordination
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Transforming Cartesian Coordinates in terms of Spherical Harmonics
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Laplace transform in spherical coordinates
  • · Replies 3 ·
Replies
3
Views
3K