## Problem on the right hand rule

The cross product $\langle1,1,0\rangle \times \langle 0,0,1\rangle$ is either in the direction of $\langle 1, -1, 0\rangle$ or $\langle -1, 1, 0 \rangle$. Without computation, which is it?
• ## Solution

Recall that
Align the fingers of your right hand in the direction of $\langle1,1,0\rangle$. If you can curl them $90$ degrees toward $\langle0,0,1\rangle$, your thumb will be pointing in the direction of $\langle1,-1,0\rangle$.
Hence, the cross product is in the direction of $\langle 1, -1, 0\rangle$.