(a) \(m \begin{pmatrix} 2 \\ 1 \end{pmatrix} + n \begin{pmatrix} -1 \\ 2 \end{pmatrix} = \begin{pmatrix} 5 \\ -4 \end{pmatrix}\) where m and n are scalars. ...

(a) \(m \begin{pmatrix} 2 \\ 1 \end{pmatrix} + n \begin{pmatrix} -1 \\ 2 \end{pmatrix} = \begin{pmatrix} 5 \\ -4 \end{pmatrix}\) where m and n are scalars. Find the value of (m + n).

(b) A(-1, 3), B(2, -1) and C(5, 3) are the vertices of \(\Delta\) ABC.

(i) Express in column notation, the unit vectors parallel to AB and AC.

(ii) Use a dot product to calculate \(\stackrel \frown{BAC}\), correct to the nearest degree.