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} \$