Orientation/1 2 3 and 0 2 -2 and x 5 7/Depending on x/Exercise

We consider in ${}\mathbb {R} ^{3}$ the three vectors

${\begin{pmatrix}1\\2\\3\end{pmatrix}},\,{\begin{pmatrix}0\\2\\-2\end{pmatrix}},\,{\begin{pmatrix}x\\5\\7\end{pmatrix}}.$

a) How do we have to choose ${}x$ such that these three vectors represent the standard orientation of the ${}\mathbb {R} ^{3}$?

b) How do we have to choose ${}x$ such that these three vectors represent the orientation of the ${}\mathbb {R} ^{3}$ opposite to the standard orientation?

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