(a) Given that \(m = (6i + 8j)\) and \(n = (-8i + \frac{7}{3}j)\), find the : (i) magnitudes and direction of m and n ; (ii) angle between m and n. (b) The ...

(a) Given that \(m = (6i + 8j)\) and \(n = (-8i + \frac{7}{3}j)\), find the :

(i) magnitudes and direction of m and n ; (ii) angle between m and n.

(b) The position vectors of points P, Q, R and S are \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}, \begin{pmatrix} 10 \\ 4 \end{pmatrix}, \begin{pmatrix} 3 \\ 12 \end{pmatrix}\) and \(\begin{pmatrix} 4 \\ 0 \end{pmatrix}\) respectively. Show that \(\overrightarrow{PQ}\) is perpendicular to \(\overrightarrow{RS}\).