Exercise 54

If \(\mathbf{r} = \langle x, y, z \rangle, \mathbf{a} = \langle a_1, a_2, a_3 \rangle,\) and \(\mathbf{b} = \langle b_1, b_2, b_3 \rangle\), show that the vector equation \((\mathbf{r} - \mathbf{a}) \cdot (\mathbf{r} - \mathbf{b}) = 0\) represents a sphere, and find its center and radius.