2022 ACJC P1 Q3

With reference to the origin \(O\), the points \(A\), \(B\) and \(C\) have position vectors \(\mathbf{a}\), \(\mathbf{b}\) and \(\mathbf{c}\) respectively, where points \(O\), \(A\), \(B\) and \(C\) are not collinear.

1. It is given that that \(\left| \mathbf{a} \right|=\sqrt{10}\), \(\left| \mathbf{b} \right|=20\), \(\mathbf{a}\cdot \mathbf{b}=40\) and the point \(N\) has position vector \(\frac{5\mathbf{a}+3\mathbf{b}}{8}\). Find the exact area of triangle \(ONB\).[5]
2. Find the angle between the vector \(\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}\) and the plane \(\pi \) containing points \(A\), \(B\) and \(C\).[2]