Suppose you are given a vector space of $\mathbb{R}^3$ and a vector space $U \subseteq \mathbb{R}^3$. Let $x\in\mathbb{R}^3$
Now suppose \begin{equation}U=span(u_1, u_2)\end{equation} and \begin{equation}x=u_2\end{equation}
Obviously : \begin{equation}x = 0\times u_1 + 1\times u_2\end{equation}
Thus, if I understand it correctly the concept of projection, as $u_2 \in span(u_1, u_2)$ the projection $\pi_U$ of $x$ on $U$ is $x$ itself, i.e. $\pi_U(x)=x$ ?
Hence the distance between $x$ and $U$ would be $d(x, U)=0$ as $x$ is already on the span of $U$ ?
Does the vector \begin{equation}c=\begin{bmatrix}0 \\ 1\end{bmatrix}\end{equation} which represents the coefficients of the linear combination to get to $u_2$ should be interpreted in any way ?