5 The vectors \(\mathbf { p }\) and \(\mathbf { q }\) are given by
$$\mathbf { p } = 8 \mathbf { i } + \mathbf { j } \text { and } \mathbf { q } = 4 \mathbf { i } - 7 \mathbf { j } .$$
- Show that \(\mathbf { p }\) and \(\mathbf { q }\) are equal in magnitude.
- Show that \(\mathbf { p } + \mathbf { q }\) is parallel to \(2 \mathbf { i } - \mathbf { j }\).
- Draw \(\mathbf { p } + \mathbf { q }\) and \(\mathbf { p } - \mathbf { q }\) on the grid.
Write down the angle between these two vectors.