Find the obtuse angle between the vectors \(\overrightarrow { O A }\) and \(\overrightarrow { O B }\).
The line \(l\) passes through the points \(A\) and \(B\).
Find a vector equation for the line \(l\).
Find the position vector of the point of intersection of the line \(l\) and the line passing through \(C\) and \(D\).
11 Let \(\mathrm { f } ( x ) = \frac { 5 x ^ { 2 } + x + 11 } { \left( 4 + x ^ { 2 } \right) ( 1 + x ) }\).
Express \(\mathrm { f } ( x )\) in partial fractions.
Hence show that \(\int _ { 0 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x = \ln 54 - \frac { 1 } { 8 } \pi\).
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.