7. A force \(\mathbf { F }\) is given by \(\mathbf { F } = ( 9 \mathbf { i } + 13 \mathbf { j } )\) N.
- Find the size of the angle between the direction of \(\mathbf { F }\) and the vector \(\mathbf { j }\).
The force \(\mathbf { F }\) is the resultant of two forces \(\mathbf { P }\) and \(\mathbf { Q }\). The line of action of \(\mathbf { P }\) is parallel to the vector ( \(2 \mathbf { i } - \mathbf { j }\) ). The line of action of \(\mathbf { Q }\) is parallel to the vector ( \(\mathbf { i } + 3 \mathbf { j }\) ).
- Find, in terms of \(\mathbf { i }\) and \(\mathbf { j }\),
- the force \(\mathbf { P }\),
- the force \(\mathbf { Q }\).