question_answer

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) \[\lambda \in R-\{0\}\]