# Direction of E-Field in 3d space

1. Oct 31, 2014

### Zaent

1. The problem statement, all variables and given/known data
I am trying to find the direction of an E-Field from a given E-Field vector in 3d space.
If I have an electric field vector of (-1i, -2j, 3k), the magnitude of the field is sqrt(-1^2 + -2^2 + 3^2) = 3.74, but how do I find the direction?

2. Relevant equations
tan(y/x)?

3. The attempt at a solution
In 2d space I understand that the direction would be presented as an angle in relation to the positive x-axis. e.g. E-Field is 1000 N/C, 90 degrees counterclockwise from +x-axis.

I am lost as to how this is both calculated and presented in 3 dimensions, however.

2. Oct 31, 2014

### Staff: Mentor

Think in terms of spherical coordinates which means you need two angles one relative to the z axis as an example.

3. Nov 1, 2014

### quantumtimeleap

Just specifying the vector completely (not just its magnitude) automatically gives the direction of the vector. You expressed the vector in Cartesian unit vectors. That already gives its direction. We have to know exactly what the problem is asking for.

A more well-phrased question could be answered precisely. For example:

1.) Express the direction in terms of the Euler angles.
2.) Like jedishrfu said above, express the direction in terms of $\theta$ and $\phi$ in spherical polar coordinates.
3.) Express the direction as a linear combination of the three Cartesian unit vectors.

For (1.) and (2.) you can google the formulas. For (3) simply divide the vector by its norm (length).

4. Nov 1, 2014