3
- 6
p
\end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { r }
2
- 6
- 7
\end{array} \right)$$
and angle \(A O B = 90 ^ { \circ }\).
- Find the value of \(p\).
The point \(C\) is such that \(\overrightarrow { O C } = \frac { 2 } { 3 } \overrightarrow { O A }\). - Find the unit vector in the direction of \(\overrightarrow { B C }\).
3 - Prove the identity \(\frac { 1 + \cos \theta } { \sin \theta } + \frac { \sin \theta } { 1 + \cos \theta } \equiv \frac { 2 } { \sin \theta }\).
- Hence solve the equation \(\frac { 1 + \cos \theta } { \sin \theta } + \frac { \sin \theta } { 1 + \cos \theta } = \frac { 3 } { \cos \theta }\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).