Let (Pi) be the plane in (R^{3}) spanned by vectors (boldsymbol{x}_{1}=(1,2,2)) and (boldsymbol{x}_{2}=) ((-1,0,2)). (i) Find an
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Let \(\Pi\) be the plane in \(R^{3}\) spanned by vectors \(\boldsymbol{x}_{1}=(1,2,2)\) and \(\boldsymbol{x}_{2}=\) \((-1,0,2)\).
(i) Find an orthonormal basis for \(\Pi\).
(ii) Extend it to an orthonormal basis for R3.
Let \(\boldsymbol{x}_{3}=(0,0,1)\).
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