In this video you are shown the conditions for two lines to be parallel and given the following question to answer.

Solve:

  1. \text{If the lines } l_1 : \bf{r} = \left( {\begin{array} {*{20}{c}} 1\\ -5\\ 7} \end{array}} \right) + \lambda \left( {\begin{array}{*{20}{c}} {a - 1}\\ {-a-1}\\ b \end{array}} \right) \\ \\ \\ \text{ and } l_2 : \bf{r} = \left( {\begin{array}{*{20}{c}} 9\\ 3\\ {-8} \end{array}} \right) + \mu \left( {\begin{array}{*{20}{c}} {2a}\\ {3 - 5a}\\ {15} \end{array}} \right) {\text{ are parallel.}} \\ \\ \\ {\text{Find the values of }}a{\text{ and }}b.