# What does it mean if you take the zero vector in the hyperplane separation theorem?

If you have two disjoint sets V and W, which are compact and convex, then by the separation theorem there exists a vector u such that uv< uw.

However what does it mean if you take u=0?

• The theorem states that there exists a $u$; you cannot choose it. – angryavian Jan 15 at 20:35
• The separation theorem gives the existence of a non zero $u$. – copper.hat Jan 15 at 20:37
• If $u=0$ then $uv\not\lt uw$. – John Douma Jan 15 at 21:03