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

In summary, the conversation discusses converting vectors to spherical coordinates at a given point. The formula for converting x, y, z into r, θ, φ is mentioned, and the process for finding the values of θ, φ, and r is also discussed. There is also a mention of finding a more objective solution and a request for assistance in deleting a post.
  • #1
Dong Hoon Lee
4
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 !
 
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  • #2
I want to know how to chage between sehperical coordinates and cartesian coordinates
 
  • #3
I am sorry that I posted wrong forum,,, how can i erase my post?
 

1. How do you transform vectors to spherical coordinates?

To transform vectors to spherical coordinates, you can use the following formula:
r = √(x² + y² + z²)
θ = arccos(z/r)
φ = arctan(y/x)

2. What are the benefits of using spherical coordinates?

One benefit of using spherical coordinates is that they are useful for describing positions on a sphere or a curved surface. They are also convenient for solving certain types of physics and engineering problems, such as those involving forces or electric fields.

3. What is the difference between spherical and Cartesian coordinates?

Spherical coordinates use a distance, an angle measured from the positive z-axis, and an angle measured from the positive x-axis, to define a point in three-dimensional space. Cartesian coordinates, on the other hand, use three perpendicular axes (x, y, and z) to define a point. Spherical coordinates are especially useful for describing points on curved surfaces, while Cartesian coordinates are more commonly used for describing points in a flat coordinate system.

4. How do you convert from Cartesian coordinates to spherical coordinates?

To convert from Cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ), you can use the following formulas:
r = √(x² + y² + z²)
θ = arccos(z/r)
φ = arctan(y/x)

5. What are some real-world applications of spherical coordinates?

Spherical coordinates are commonly used in navigation systems, such as GPS, to determine the position of an object on the Earth's surface. They are also used in astronomy to locate celestial objects in the sky. In physics and engineering, spherical coordinates are used to solve problems involving forces, electric fields, and fluid dynamics. They are also used in computer graphics to create three-dimensional images and animations.

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