Problem $1.$ Determine whether the lines parametrized by vec$(r)(t)=($:$2,3,0$:$)+t($:$1,2,1$:$)$ and vec$(s)(t)=($:$0,-1,-2$:$)+t($:$2,4,2$:$)$ parametrize the same line, have a single point of intersection, or are disjoint.