Let Line x be defined by $\displaystyle \bar {p_{1}}(t) = \bar {p_{1}}+t \bar {V_{1}} $ and

let Line y be defined by $\displaystyle \bar {p_{2} }(s) = \bar {p_{2}} + s \bar {V_{2}} $

Find conditions on line x,y such that they have unique point of intersection. Find this point.

Would that be $\displaystyle \bar {V_{1}} \dot \bar {V_{2}} \neq 0 $? And how would I find the point?