5 You are given the variable point \(A ( 3 , - 8 , t )\), where \(t\) is a real parameter, and the fixed point \(B ( 1,2 , - 2 )\).
- Using only the geometrical properties of the vector product, explain why the statement " \(\overrightarrow { \mathrm { OA } } \times \overrightarrow { \mathrm { OB } } = \mathbf { 0 }\) " is false for all values of \(t\).
- Use the vector product to find an expression, in terms of \(t\), for the area of triangle \(O A B\).
- Hence determine the value of \(t\) for which the area of triangle \(O A B\) is a minimum.