Studying outer product spaces at the moment and thought I'd quickly recap on the cross product when I stumbled across this problem which has me fairly stumped! If a,b∈R^3 with a≠0 show that the equation a x u = b has a solution if and only if a.b = 0 and find all the solutions in this case. The answer is, -((a x b)/|a|^2) + λ a , where λ is a real parameter. The first part is trivial, but I have no idea how to get to the solution set. Could anybody shed any light on this matter? I would be very grateful.