Consider $\mathbb R^4$ together with the standard inner product and let $W=\{(x_1, x_2, x_3, x_4) \in \mathbb R^4 |\ x_1+x_2-x_4=0\}$. Find a basis for $W^\perp$.
How do you solve this question? All I can think of is that you have to put the elements in $W$ in terms of others.