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- #1

Show that $(\mathbf{x} - \mathbf{b})\cdot\mathbf{x} = 0$ is the vector equation of a spherical surface having its center at $\mathbf{x} = \frac{1}{2}\mathbf{b}$ with radius of $\frac{1}{2}b$.

\begin{alignat}{3}

(x_i\hat{\mathbf{e}}_i - b_i\hat{\mathbf{e}}_i)\cdot x_i\hat{\mathbf{e}}_i & = & x_i^2-b_ix_i

\end{alignat}

How am I supposed to obtain that $b_i = x_i$?