6 The points \(A\) and \(B\) have coordinates \(( 2,4,1 )\) and \(( 3,2 , - 1 )\) respectively. The point \(C\) is such that \(\overrightarrow { O C } = 2 \overrightarrow { O B }\), where \(O\) is the origin.
- Find the vectors:
- \(\overrightarrow { O C }\);
- \(\overrightarrow { A B }\).
- Show that the distance between the points \(A\) and \(C\) is 5 .
- Find the size of angle \(B A C\), giving your answer to the nearest degree.
- The point \(P ( \alpha , \beta , \gamma )\) is such that \(B P\) is perpendicular to \(A C\).
Show that \(4 \alpha - 3 \gamma = 15\).