Standard +0.3 Part (ii) is a standard verification that two lines are skew by showing no common solution exists for their parametric equations—a routine C4 technique requiring algebraic manipulation but no novel insight. This is slightly above average difficulty due to the algebraic work involved, but remains a textbook exercise.
9
\end{array} \right) + t \left( \begin{array} { c }
2
- 3
1
\end{array} \right)$$
(ii) Show that lines \(l _ { 1 }\) and \(l _ { 2 }\) do not intersect.
(iii) Find the position vector of the point \(C\) on \(l _ { 2 }\) such that \(\angle A B C = 90 ^ { \circ }\).
8. \(f ( x ) = \frac { 5 - 8 x } { ( 1 + 2 x ) ( 1 - x ) ^ { 2 } }\).
(i) Express \(\mathrm { f } ( x )\) in partial fractions.
(ii) 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.
(iii) State the set of values of \(x\) for which your expansion is valid.
9
\end{array} \right) + t \left( \begin{array} { c }
2 \\
- 3 \\
1
\end{array} \right)$$
(ii) Show that lines $l _ { 1 }$ and $l _ { 2 }$ do not intersect.\\
(iii) Find the position vector of the point $C$ on $l _ { 2 }$ such that $\angle A B C = 90 ^ { \circ }$.\\
8. $f ( x ) = \frac { 5 - 8 x } { ( 1 + 2 x ) ( 1 - x ) ^ { 2 } }$.\\
(i) Express $\mathrm { f } ( x )$ in partial fractions.\\
(ii) 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.\\
(iii) State the set of values of $x$ for which your expansion is valid.
\hfill \mbox{\textit{OCR C4 Q9}}