Section 12.2: Vectors

If \(\mathbf{r} = \langle x, y \rangle, \mathbf{r}_1 = \langle x_1, y_1 \rangle,\) and \(\mathbf{r}_2 = \langle x_2, y_2 \rangle\), describe the set of all points \((x, y)\) such that \(|\mathbf{r} - \mathbf{r}_1| + |\mathbf{r} - \mathbf{r}_2| = k\), where \(k > |\mathbf{r}_1 - \mathbf{r}_2|\).