Question
Let $ \vec{a} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k} $, and $ \vec{b} $ be a vector such that $ \vec{a} \cdot \vec{b} = |\vec{b}|^2 $ and $ |\vec{a} - \vec{b}| = \sqrt{7} $. Then, $ |\vec{b}| = $
Let $ \vec{a} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k} $, and $ \vec{b} $ be a vector such that $ \vec{a} \cdot \vec{b} = |\vec{b}|^2 $ and $ |\vec{a} - \vec{b}| = \sqrt{7} $. Then, $ |\vec{b}| = $