Here is an example of an equation in the algebra of vectors.

Let \\(x\\) stand for an unknown vector in \\(\mathbb{R^3}\\).

Now solve for \\(x\\) in the equation:

\\[
x
+
\begin{bmatrix}
10 \\\\ 20 \\\\ 30 \\\\
\end{bmatrix}
=
\begin{bmatrix}
0 \\\\ 0 \\\\ 0 \\\\
\end{bmatrix}
\\]