1 The points \(A , B\) and \(C\) have position vectors \(\mathbf { a } = \left( \begin{array} { l } 3
0
0 \end{array} \right) , \mathbf { b } = \left( \begin{array} { l } 0
4
0 \end{array} \right)\) and \(\mathbf { c } = \left( \begin{array} { l } 0
0
1 \end{array} \right)\) respectively, relative to the origin \(O\).

1. 1. Calculate \(\mathbf { a } \times \mathbf { b }\), giving your answer as a multiple of \(\mathbf { c }\).
   2. Explain, geometrically, why \(\mathbf { a } \times \mathbf { b }\) must be a multiple of \(\mathbf { c }\).
2. Use a vector product method to calculate the area of triangle \(A B C\).