Past exam of the mathematical methods I course of the University of Oxford / 2015 / 10 / a / i / Solution

In one dimension the nonzero vector $b$ already spans the real line. Hence $\mathrm{span}(b,c)=\mathbb{R}$, and translating it by $a$ leavesThis is an affine subspace containing the origin for every allowed choice of the three vectors.