2023 TYS

Vectors $\mathbf{a}$ and $\mathbf{b}$ are such that $\mathbf{a}\cdot \mathbf{b}=-1$. It is also given that $\left( \mathbf{a}\times \mathbf{b}+\mathbf{a} \right)$is perpendicular to $\left( \mathbf{a}\times \mathbf{b}+\mathbf{b} \right)$.

1. Show that $\left| \mathbf{a}\times \mathbf{b} \right|=1$.

   [3]

2. Hence, find the angle between the direction of $\mathbf{a}$and the direction of $\mathbf{b}$.

   [3]