Solution
= Solution
The <affine subspace> is $S=a+\operatorname{span}(b,c)$. If $b,c$ are <linearly independent>, their <linear span> is all of $\mathbb R^2$, so \b[$S$ is the whole plane]. If they are proportional, \b[$S$ is the line through $a$ in direction $b$]. This line passes through the origin exactly when $a\in\operatorname{span}(b)$. Because $b$ is nonzero, the set cannot be a single point.