Consider parallelogram ABCD with points S and T chosen such that \(CS:SD = BT:TC = 2\)

as in the picture below:

Let \(\overrightarrow{AB} = \mathbf{v}\) and \(\overrightarrow{AD} = \mathbf{w}\). Then there exist constants r, s, t, u such that \(\begin{align*} \overrightarrow{AT} &= r \mathbf{v} + s \mathbf{w},\\ \overrightarrow{BS} &= t \mathbf{v} + u \mathbf{w}. \end{align*}\)

Enter r, s, t, u in that order below.

Guest Apr 4, 2019