It will prove convenient to express the dot product in a form where its left input is a row vector, and its right input is a column vector.

So we would write:

\\[
\begin{bmatrix}
1 & 2
\end{bmatrix}
\cdot
\begin{bmatrix}
10 \\\\
20
\end{bmatrix}
=
1 \cdot 10 + 2 \cdot 20 =50
\\]