Mathematics

Problem

Let

\mathbf{a}

and

\mathbf{b}

be non-zero vectors such that

|\mathbf{a}| = 3|\mathbf{b}|

and the angle between them is

\theta

. If

\mathbf{a}\cdot\mathbf{b} = |\mathbf{b}|^{2}

, determine the following: a. (i) the value of

\cos\theta

b. (ii) the angle

\theta