Two lines in space are given by … and

Two lines in space are given by $\mathbf{R}(t)=\mathbf{P}+t\mathbf{v}$ and $\mathbf{R}(t)=\mathbf{Q}+t\mathbf{w}$. Four possibilities: The lines are parallel or the same or intersecting or skew. Decide which is which based on the vectors $\mathbf{v}$ and $\mathbf{w}$ and $\mathbf{u}=\mathbf{Q}-\mathbf{P}$ (which goes between the lines):
(a) The lines are parallel if ____ are parallel.
(b) The lines are the same if ____ are parallel.
(c) The lines intersect if ____ are not parallel but ____ lie in the same plane.
(d) The lines are skew if the triple product $\mathbf{u}\cdot (\mathbf{v}\times \mathbf{w})$ is ____.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.1 The Position Vector, #41