9 \end{array} \right) + \mu \left( \begin{array} { c } 2
- 3
1 \end{array} \right)$$ (b) Show that lines \(l _ { 1 }\) and \(l _ { 2 }\) do not intersect.
(c) Find the position vector of the point \(C\) on \(l _ { 2 }\) such that \(\angle A B C = 90 ^ { \circ }\).
7. continued
8. $$f ( x ) = \frac { x ( 3 x - 7 ) } { ( 1 - x ) ( 1 - 3 x ) } , | x | < \frac { 1 } { 3 }$$ (a) Find the values of the constants \(A , B\) and \(C\) such that $$\mathrm { f } ( x ) = A + \frac { B } { 1 - x } + \frac { C } { 1 - 3 x }$$ (b) Evaluate $$\int _ { 0 } ^ { \frac { 1 } { 4 } } f ( x ) d x$$ giving your answer in the form \(p + \ln q\), where \(p\) and \(q\) are rational.
(c) Find the series expansion of \(\mathrm { f } ( x )\) in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), simplifying each coefficient.
8. continued
8. continued