4
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r }
4
2
- 2
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { l }
1
3
p
\end{array} \right)$$
Find
- the unit vector in the direction of \(\overrightarrow { A B }\),
- the value of the constant \(p\) for which angle \(B O C = 90 ^ { \circ }\).
3 The first three terms in the expansion of \(( 1 - 2 x ) ^ { 2 } ( 1 + a x ) ^ { 6 }\), in ascending powers of \(x\), are \(1 - x + b x ^ { 2 }\). Find the values of the constants \(a\) and \(b\).
4
- Solve the equation \(\sin 2 x + 3 \cos 2 x = 0\) for \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).
- How many solutions has the equation \(\sin 2 x + 3 \cos 2 x = 0\) for \(0 ^ { \circ } \leqslant x \leqslant 1080 ^ { \circ }\) ?