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I found a very helpful post about exactly what I need here. It uses dot products to which is what I'm specifically looking for.
It talks about players facing monsters basically. They give a helpful picture here, 
My question though, is what if you have a function with 3 arguments: the position of object 1, the position of object 2, and the direction object 1 is facing given as a unit vector. So the picture would look as so:
How would you find whether A is facing B?
It depends on exactly what you mean by "A is facing B", but you can use the same approach mentioned in the link you give. The other vector to examine (in addition to the direction A is facing) is the one connecting and pointing from A to B (calculated by B-A).
Your code would be something like.
facing = dotProduct(normalize(B-A), normalize(directionFacingOfA))
Which will give you the cosine of the angle between where A is facing, and the vector where A faces B. Pretty easy. Three possibilities:
A faces B almost perfectly (angle close to 0), facing will be close to 1 (cos(0)). A isn't facing away from B, facing will be between 0 and 1. It is up to you to decide if this is "close enough".A is facing away from B, facing will be negative. This approach works for either 2D or 3D.
