On $S^{1}$ there are three choices for a vector pointed inward to the same angle at the tangent line at every point. The vector is either in the opposite direction as the normal, or to the left of it, or to the right of it. (clockwise, counterclockwise, and all inward)
I can skip $S^{2}$ because of the hairy ball theorem. What about $S^{3}$ and $S^{7}$? I know that they're both uncombable.