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Find the (orthogonal) projection of $\mathbf{x}:=(1,2,0)$ into the following subspaces:
a) The line spanned by $\mathbf{u}:=(1,1,-1)$.
b) The plane spanned by $\mathbf{u}:=(0,1,0)$ and $\mathbf{v}:=(0,0,-2)$
c) The plane spanned by $\mathbf{u}:=(0,1,1)$ and $\mathbf{v}:=(0,1,-2)$
d) The plane spanned by $\mathbf{u}:=(1,0,1)$ and $\mathbf{v}:=(1,1,-1)$
e) The plane spanned by $\mathbf{u}:=(1,0,1)$ and $\mathbf{v}:=(2,1,0)$.
f) The subspace spanned by $\mathbf{u}:=(1,0,1), \mathbf{v}:=(2,1,0)$ and $\mathbf{w}:=(1,1,0)$.
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