vectors in spherical coordinates

[Random Variable]

The unit vector k crossed with the position vector x in cartesian coordinates is (-y,x,0). In sperhical coordinates it's (0,0,?sin?). The unit vector k crossed with the positon vector x (which is (?,0,0) in spherical coordinates) points in the positive f-direction. That I understand. But why the ?sin? which is the distance from the z-axis to the position vector?


What I did was first find the vector in cartesian coordinates and then convert it to spherical coordinates using matrix multiplication. I got the correct answer, but it can get awfully tedious.

EDIT: Oh. nevermind. I get it. |k X x| = |k||x|*sin of the angle between them = 1*?*sin?.
And it points in the f-direction. I'm so stupid. 😱

 

[chuckywang]

The position vector x is not (p,0,0) in spherical coordinates.

 

[DVK916]

The answer is 42.

 

[Random Variable]

Originally posted by: chuckywang
The position vector x is not (p,0,0) in spherical coordinates.

Of course it is. In cartesian it's (x,y,z); in cylindrical it's (r,0,z); and in spherical it's (?,0,0).

 

[SagaLore]

z axis is z answer.

 

[chuckywang]

Originally posted by: Random Variable

Originally posted by: chuckywang
The position vector x is not (p,0,0) in spherical coordinates.

Of course it is. In cartesian it's (x,y,z); in cylindrical it's (r,0,z); and in spherical it's (?,0,0).

(p,0,0) says that theta=0 and phi=0. Therefore, the vector is on the positive z-axis. BTW, you shouldn't label vectors as x since it can be confused with the vector component in thie x direction.

 

[Random Variable]

Originally posted by: chuckywang

Originally posted by: Random Variable

Originally posted by: chuckywang
The position vector x is not (p,0,0) in spherical coordinates.

Of course it is. In cartesian it's (x,y,z); in cylindrical it's (r,0,z); and in spherical it's (?,0,0).

(p,0,0) says that theta=0 and phi=0. Therefore, the vector is on the positive z-axis. BTW, you shouldn't label vectors as x since it can be confused with the vector component in thie x direction.

Most physics textbooks label the position vector as x. And what is the position vector in spherical coordinates?

 

[GreenGhost]

Kids and their homework 🙂

 

[Muse]

I think the Highly Technical Forum is a better place for this that ATOT.