= Solution
The nonzero <vectors> $b,c$ are <normal vectors> to the two <planes>. If $b\times c=0$, then $c=qb$ for some nonzero real $q$. Their equations are therefore $r\cdot b=\lambda$ and $q(r\cdot b)=\mu$.
When $\mu=q\lambda$, the <planes> coincide and their intersection is an entire <plane>. Otherwise they are distinct parallel planes and have no intersection. Neither case has exactly a <line> as its intersection. Hence \b[$b\times c\ne0$ is necessary] for intersection in a <line>. It means that the two <normal vectors> are not parallel; in that case it is also sufficient.
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