Two Orders, Two Landing Points

You are given two $2 \times 2$ matrices:

$A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}, \qquad B = \begin{bmatrix} 3 & 0 \\ 1 & 2 \end{bmatrix}$

Form both products,

$P = AB \qquad \text{and} \qquad Q = BA$

and apply each one to the same vector

$\vec{v} = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$

The results $P\vec{v}$ and $Q\vec{v}$ are two points in the plane. Report the straight-line (Euclidean) distance between those two points.

Round your answer to two decimal places.