6
4
\end{array} \right) + s \left( \begin{array} { l }
3
2
1
\end{array} \right) \quad \text { and } \quad \mathbf { r } = \left( \begin{array} { l }
1
0
0
\end{array} \right) + t \left( \begin{array} { r }
0
1
- 1
\end{array} \right)$$
respectively.
- Show that \(l _ { 1 }\) and \(l _ { 2 }\) are skew.
- Find the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\).
- The point \(A\) lies on \(l _ { 1 }\) and \(O A\) is perpendicular to \(l _ { 1 }\), where \(O\) is the origin. Find the position vector of \(A\).
6 Find the coefficient of \(x ^ { 2 }\) in the expansion in ascending powers of \(x\) of
$$\sqrt { \frac { 1 + a x } { 4 - x } } ,$$
giving your answer in terms of \(a\).