Let A ( a ) and B ( b ) be points on two skew lines r = a + p and r = b + u q and the…

Let A \((\overrightarrow{\mathrm{a}})\) and B \((\overrightarrow{\mathrm{b}})\) be points on two skew lines \(\overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a}}+\lambda \overrightarrow{\mathrm{p}}\) and \(\overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{b}}+\mathrm{u} \overrightarrow{\mathrm{q}}\) and the shortest distance between the skew lines is 1, where \(\overrightarrow{\mathrm{p}}\) and \(\overrightarrow{\mathrm{q}}\) 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°, then AB =