Converting F to Cartesian Coordinates

[DarkSamurai]

Homework Statement

Convert F into cartesian coordinates from spherical
F = -4*theta*e_r + 1e_phi
r(t) = 2, theta(t) = 4t, phi(t) = pi / 2

Homework Equations

x = rsin(theta)cos(phi)
y = rsin(theta)sin(phi)
z = rcos(phi)

The Attempt at a Solution

Where I'm having problem is converting F into Cartesian coordinates.

 

[Mark44]

What do e_r and 1e_phi mean in this equation?
F = -4*theta*e_r + 1e_phi

 

[DarkSamurai]

e_r and e_theta are the unit vectors... for the coordinate system I believe.

$$\hat{e_{r}}$$ and $$\hat{e_{\theta}}$$

 

[Mark44]

You have an error in your conversion formulas, at least if you're using theta and phi in their usual meanings. The formulas should be:
x = rho* sin(phi)*cos(theta)
y = rho*sin(phi)*sin(theta)
z = rho*cos(phi)

Compare the formulas for x and y with the ones you have in your first post. Phi is the angle between the z-axis and the vector to the point (rho, theta, phi). If you project this vector onto the x-y plane, you get a vector of length r, where r = rho*sin(phi). Theta is the angle between this projected vector and the x-axis.

Haven't run into the unit vectors e_r and e_phi before. Since they're unit vectors, their magnitutes must be 1. What about their directions? I would guess that e_r (really e_rho) is a unit vector with the same direction as the vector from the origin to the point (rho, theta, phi). Is that correct? I can't picture what direction e_phi points if it's some direction other than the direction for e_rho. Can you provide definitions for these unit vectors?