>>11451185you posted the picture in your op... just because you know the resulting vector is on the z-axis doesn't mean you know whether it points up or down. you can use the right hand rule to figure it out. just point your right index finger in the direction of A and then see whether B points from your palm or from the back of your hand. if from the back of your hand, you'll need to flip your hand and then your thumb will point down. here, B points from your palm so the resulting vector goes up.
the formal point of this is that the basis vectors i, j, k in R^3 have an "orientation," that is a standard ordering. here it's just (i, j, k). this ordering determines things like the sign of cross products, the curvature properties of a curve, and the way you find how a flow moves through a surface.
