I was reading Bombshell and they talked about how Ted Hall figured out how cross products worked before his brother who had 2 engineering degrees. The cross product was one the the first "engineering concepts" I learned in college and pretty essential to understanding engineering in general.
Engineering student here. First, I have a book called "building an engeneering career" from 1936. I will look through it when I get a chance. Secondly, and this is speculative, might the elder brother be familiar with quaternions? They were a strange way of representing vectors that fell out of favor around 1900. I've seen a mechanics book from about that time that forcefully argued in favor of vectors as we know them. So if the elder brother had a stubborn professor it's possible that he was unfamiliar with the cross product in the form that we know.
A ww2 era electricity book I have explains the cross product just fine, and it's aimed at technicians more than engineers. Perhaps the deeper meaning of the cross product with relation to matrices was what the younger brother understood? I know linear algebra was deempasized before digital computers.