# I have to prove that vectors in spherical coordinates are clockwise

• Danielle46
In summary, the conversation discusses the use of cross product and the formation of a right-handed orthonormal basis in spherical coordinates. The person also mentions a task involving proving the clockwise direction of vectors in spherical coordinates.
Danielle46 said:
Homework Statement:: I have to prove that vectors in spherical coordinates are clockwise.
I have to admit. I don't even know what this means.

berkeman

## 1. What are spherical coordinates?

Spherical coordinates are a system of coordinates used to locate points in three-dimensional space. They consist of a distance (r) from the origin, an angle (θ) from the positive z-axis, and an angle (φ) from the positive x-axis.

## 2. How do you convert vectors from Cartesian coordinates to spherical coordinates?

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

## 3. Are vectors in spherical coordinates always clockwise?

No, vectors in spherical coordinates can be either clockwise or counterclockwise, depending on their direction and the orientation of the coordinate system.

## 4. How do you prove that vectors in spherical coordinates are clockwise?

To prove that a vector in spherical coordinates is clockwise, you can use the right-hand rule. If you curl your fingers in the direction of the vector, your thumb should point in the direction of the positive z-axis, which is considered clockwise.

## 5. Can vectors in spherical coordinates be negative?

Yes, vectors in spherical coordinates can have negative components, just like in Cartesian coordinates. The direction and magnitude of the vector are determined by its components, regardless of whether they are positive or negative.

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