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!(adsbygoogle = window.adsbygoogle || []).push({});

Ifa,b∈R^3witha≠0show that the equationa x u = bhas a solution if and only ifa.b= 0 and find all the solutions in this case.

The answer is,

-((a x b)/|a|^2) +λa, whereλis 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solutions to cross product, a x u = b

**Physics Forums | Science Articles, Homework Help, Discussion**