= Solution
The <position vectors> end at the midpoints of $BC$, $CA$ and $AB$, respectively. The drawing places $E$, $F$ and $G$ on those edges and shows the arrows from the origin. The volume of their <parallelepiped> is the absolute <scalar triple product>:
$$
\mathbf e\times\mathbf f=\left(\frac14,\frac14,-\frac14\right),\qquad
V=|(\mathbf e\times\mathbf f)\cdot\mathbf g|=\boxed{\frac14}.
$$
Equivalently, this is the absolute <determinant> of the matrix whose columns are the three vectors. Since it is nonzero, the vectors are <linearly independent>. Three <linearly independent> vectors in the three-dimensional <vector space> $\mathbb R^3$ form a <basis>.
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