How do I calculate $\left \| \vec{v}-\vec{u} \right \|_2$ for $\vec{u}\in U$?

Question

Let $U=\lambda ((1, 0, 1, 0)^T,(1, 1, 0, 1)^T,(1, -1, 1; 0)^T)$ Is a subspace of $\mathbb{R}^4$. Determine for $\vec{v} = (1, 1, 1, 1)^T$ the vector $ \vec{u}\in U $ with minimal $\left \| \vec{v}-\vec{u} \right \|_2 $. $\vec{u}= \left (\vec{v} · \vec{b_1} \right )\vec{b_1} + \left (\vec{v} · \vec{b_2} \right )\vec{b_2}+\left (\vec{v} · \vec{b_3} \right )\vec{b_3}$