This exercise is from Bazaraa Linear programming book.
And I don't see the point of the exercise since the definition of direction is already given by hypothesis.
Am I missing something or the exercise it's not well stated?
Let $S$ be a closed convex set in $\mathbb R^n$ and let $x\in S$ . Suppose that $d$ is a nonzero vector in $\mathbb R^n$ and that $x +\lambda d\in S$ for all $\lambda\ge 0$. Show that $d$ is a direction of $S.$