2022 EJC J2 MYE P1 Q2

Vectors \(\mathbf{a}\),\(\mathbf{b}\) and \(\mathbf{c}\) are such that \(\mathbf{a}\ne \mathbf{0}\), \(2\mathbf{b}\ne 3\mathbf{c}\), and \(2\mathbf{a}\mathbf{.b}=3\mathbf{a}\mathbf{.c}\).

1. Show that \(\mathbf{a}\) is perpendicular to \(2\mathbf{b}-3\mathbf{c}\).[2]
2. It is now given that \(\mathbf{b}\) is a unit vector, that the modulus of \(\mathbf{c}\) is \(\frac{4}{3}\) and that \(\mathbf{a}\) is parallel to \(\mathbf{b}\). Find the angle between \(\mathbf{b}\) and \(\mathbf{c}\).[3]