5
1
3
\end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { r }
5
4
- 3
\end{array} \right) .$$
The point \(P\) lies on \(A B\) and is such that \(\overrightarrow { A P } = \frac { 1 } { 3 } \overrightarrow { A B }\).
- Find the position vector of \(P\).
- Find the distance \(O P\).
- Determine whether \(O P\) is perpendicular to \(A B\). Justify your answer.
5 - Show that the equation \(\frac { 2 \sin \theta + \cos \theta } { \sin \theta + \cos \theta } = 2 \tan \theta\) may be expressed as \(\cos ^ { 2 } \theta = 2 \sin ^ { 2 } \theta\).
- Hence solve the equation \(\frac { 2 \sin \theta + \cos \theta } { \sin \theta + \cos \theta } = 2 \tan \theta\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).