\text { Suppose } \vec{u}=(1,0,-1,-1), \vec{v}=(0,1,-1,1), \text { and } \vec{w}=(1,1,1,0) . \text { Notice that this is } \text { an orthogonal set of vectors. If } W=\operatorname{span}\{\vec{u}, \vec{v},

\vec{w}\}, \text { then write the orthogonal } \text { projection of } \vec{x}=(2,3,1,7) \text { as a linear combination of } \vec{u} \cdot \vec{v}, \text { and } \vec{w} \text { . } \operatorname{proj}(\vec{x})=---\vec{u}+---\vec{v}+---\vec{w}