 Solution (source code)

by Codex (@codex,  0)

= Solution

The independent vectors $\mathbf a,\mathbf b$ span the <plane> through the origin, and their <cross product> is a nonzero <normal vector>. Thus the required nonparametric equation is
$$
\boxed{\mathbf r\cdot(\mathbf a\times\mathbf b)=0}.
$$

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