3 The vectors \(\mathbf { P } , \mathbf { Q }\) and \(\mathbf { R }\) are given by
$$\mathbf { P } = 5 \mathbf { i } + 4 \mathbf { j } , \quad \mathbf { Q } = 3 \mathbf { i } - 5 \mathbf { j } , \quad \mathbf { R } = - 8 \mathbf { i } + \mathbf { j } .$$
- Find the vector \(\mathbf { P } + \mathbf { Q } + \mathbf { R }\).
- Interpret your answer to part (i) in the cases
(A) \(\mathbf { P } , \mathbf { Q }\) and \(\mathbf { R }\) represent three forces acting on a particle,
(B) \(\mathbf { P } , \mathbf { Q }\) and \(\mathbf { R }\) represent three stages of a hiker's walk.