Good, then it is easy, take the vector space to be 1 d, take v_1 to be the origin, take v_2 to be -1, take v_3 to be 1, then the convex hull of {v_1, v_2, v_3} is the line segment [-1, 1], the extreme point of which is v_2 = -1 and v_3 = 1. Obviously v_1 = 0 is not an extreme point (also, you may use the result we just prove that the origin is not the boundary of [-1, 1], while extreme point must be a subset of the boundary part.)