This is the code I have:
\begin{align}
\vec{l} \cdot \vec{n} & = \left \langle 1,2,3 \right \rangle$ \cdot \left \langle 3,-3,1 \right \rangle \\
& = 3 - 6 + 3 \\
& = 0 \\
\end{align}
Now for some reason, I keep getting this message:
"Missing } inserted <inserted text> } \end{align}"
I clearly have completed my }.

h; then you'll get the message "I've inserted something that you may have forgotten. (See the2and you'll get<recently read> $. So, in fact, TeX sees the problem ;-) (not as quickly as you've expected, but it sees it).\bigX,\BigX,\biggX, and\BiggXfamily of commands. Search this site for questions about\left,\rightand you'll find some discussions about whether and when to use them. – Gonzalo Medina May 13 '12 at 17:40