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\includegraphics[max width=\textwidth, alt={}, center]{32a57386-2696-4fda-a3cb-ca0c5c3be432-4_561_599_744_774} The diagram shows triangle \(O A B\), in which the position vectors of \(A\) and \(B\) with respect to \(O\) are given by $$\overrightarrow { O A } = 2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k } \quad \text { and } \quad \overrightarrow { O B } = - 3 \mathbf { i } + 2 \mathbf { j } - 4 \mathbf { k } .$$ \(C\) is a point on \(O A\) such that \(\overrightarrow { O C } = p \overrightarrow { O A }\), where \(p\) is a constant.

1. Find angle \(A O B\).
2. Find \(\overrightarrow { B C }\) in terms of \(p\) and vectors \(\mathbf { i } , \mathbf { j }\) and \(\mathbf { k }\).
3. Find the value of \(p\) given that \(B C\) is perpendicular to \(O A\).