= Solution
For the stipulated <linearly independent vectors> $\mathbf v_1,\mathbf v_2$, the denominator in part (i) is nonzero. Thus
$$
\boxed{d(L_1,L_2)=0\iff(\mathbf a_2-\mathbf a_1)\cdot(\mathbf v_1\times\mathbf v_2)=0.}
$$
Equivalently, $\mathbf a_2-\mathbf a_1$ belongs to the <linear span> of $\mathbf v_1,\mathbf v_2$. Geometrically the <lines> lie in one <plane>, and, since their direction <vectors> are not parallel, \b[they intersect at a unique <point>]. The <linear combination> expressing $\mathbf a_2-\mathbf a_1$ gives the two parameters of that intersection.
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