11 Relative to an origin \(O\), the position vectors of the points \(A\) and \(B\) are given by
$$\overrightarrow { O A } = 2 \mathbf { i } + 3 \mathbf { j } - \mathbf { k } \quad \text { and } \quad \overrightarrow { O B } = 4 \mathbf { i } - 3 \mathbf { j } + 2 \mathbf { k }$$
- Use a scalar product to find angle \(A O B\), correct to the nearest degree.
- Find the unit vector in the direction of \(\overrightarrow { A B }\).
- The point \(C\) is such that \(\overrightarrow { O C } = 6 \mathbf { j } + p \mathbf { k }\), where \(p\) is a constant. Given that the lengths of \(\overrightarrow { A B }\) and \(\overrightarrow { A C }\) are equal, find the possible values of \(p\).
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