I am aware of this Get vector components from from magnitude and angle and Finding Vectors from their angle and magnitude but they do not really solve my question.
If I have theta = 20 degrees and I am given a magnitude of m = 5 I can easily figure out the x and y components using m * cos(theta) = x and m * sin(theta) = y. However, I am not sure how this expands into 3 dimensions. Or, in other words, how would I find the z component? In the 3 dimensional case I also have access to two more angles. Theta being the angle about the z-axis, phi being the angle about the x-axis, and gamma being the angle about the y-axis.
Therefore the final question is. Given angles about the xyz axes, and a magnitude of a vector, how do I get the components x, y, and z of that vector?