Additional considerations

Magnitudes of vectors

Dimensionally uniform vector (probably) has a 2-norm (magnitude):

\[ \mathbf p = \begin{bmatrix} 1 \text{ m} \\ 2 \text{ m} \end{bmatrix} = (1 \text{ m}) \begin{bmatrix} 1 \\ 2 \end{bmatrix} \\ \lVert \mathbf p \rVert_2 = \sqrt{(1 \text{ m})^2 + (2 \text{ m})^2} = \sqrt{1 \text{ m}^2 + 4 \text{ m}^2} = \sqrt{5 \text{ m}^2} = \sqrt 5 \text{ m} \]

but otherwise no without additional care:

\[ \mathbf x = \begin{bmatrix} 1 \text{ volts} \\ 2 \text{ amperes} \end{bmatrix} \\ \lVert \mathbf x \rVert_2 = \sqrt{(1 \text{ volts})^2 + (2 \text{ amperes})^2} = \sqrt{1 \text{ volts}^2 + 4 \text{ amperes}^2} = \; ? \]