**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 $2\mathbf{a}\mathbf{.b}=3\mathbf{a}\mathbf{.c}$.

(a)

Show that $\mathbf{a}$ is perpendicular to $2\mathbf{b}-3\mathbf{c}$.

[2]

(b)

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]

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