Intersecting Spheres on a Euclidean Plane

This seems a weird question, as I can visualize it in my head, but I'm not sure how I'm supposed to answer it...

Let e3= (0,0,1) in R3. Then the sphere of radius 2 with center e3 (respectively -e3) has equation llx-e3ll = 2 (respectively, equation llx+e3ll = 2). Describe the intersection of these two spheres geometrically.

I believe that where the spheres intersect, a circle would be created. As well, I think that one can break down the llx+/-e3ll into its corresponding vector by square rooting it, but I'm not sure... There is a hint for the question, and its to use the properties of the dot product...