= Solution
Choose <Cartesian coordinates> with <unit vectors> satisfying the <right-hand rule>, $\hat{\mathbf x}\times\hat{\mathbf y}=\hat{\mathbf z}$. Put $A$, $B$ and $C$ one unit along the positive $x$, $y$ and $z$ axes, respectively. The following original drawing also includes the vectors needed in the next part.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-2-q11-basis.png]
{title=Cartesian axes and three independent midpoint position vectors}
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