Let \[A(\vec{a})\] and \[B(\vec{b})\] be points on two skew line \[\vec{r}=\vec{a}+\vec{\lambda }\] and \[\vec{r}=\vec{b}+u\vec{q}\] and the shortest distance between the skew line is 1, where \[\vec{p}\] and \[\vec{q}\] are unit vectors forming adjacent sides of a parallelogram enclosing an area of \[\frac{1}{2}\]units. If an angle between AB and the line of shortest distance is \[60{}^\circ \], then \[AB=\]

• A. \[\frac{1}{2}\]
• B. \[2\]
• C. \[1\]
• D. \[\lambda \in R-\{0\}\]