I've made mistakes where scaling was used but I just assumed that I didn't need it. e.g. a bug walking towards <1,1,1> is scaled to <1/sqrt(3), etc>. Under what kind of conditions/in what kind of problems should vectors be scaled? I know that v/|v| is the unit vector but how do I relate this to problems? Furthermore, for this problem A unit vector that is perpendicular to both v = <1; 3; 2> and w = <4; 2; 1> is... I thought would be vxw, but the answer is (1/(5sqrt(6))vxw. Why was scaling needed here?