Resultant of two forces (triangle/parallelogram law)

3 \includegraphics[max width=\textwidth, alt={}, center]{430f1f9a-7a3a-47a0-b742-daf74e68adfd-2_368_584_1302_794} Two forces, each of magnitude 10 N , act at a point \(O\) in the directions of \(O A\) and \(O B\), as shown in the diagram. The angle between the forces is \(\theta\). The resultant of these two forces has magnitude 12 N .

1. Find \(\theta\).
2. Find the component of the resultant force in the direction of \(O A\).

2 \includegraphics[max width=\textwidth, alt={}, center]{01e73486-5a95-4e65-bf18-518d1adc7cfb-2_318_632_482_753} Forces of magnitudes 13 N and 14 N act at a point \(O\) in the directions shown in the diagram. The resultant of these forces has magnitude 15 N . Find

1. the value of \(\theta\),
2. the component of the resultant in the direction of the force of magnitude 14 N .

2. \begin{figure}[h] \end{figure} Two forces \(\mathbf { P }\) and \(\mathbf { Q }\), act on a particle. The force \(\mathbf { P }\) has magnitude 5 N and the force \(\mathbf { Q }\) has magnitude 3 N . The angle between the directions of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(40 ^ { \circ }\), as shown in Fig. 1. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(\mathbf { F }\).

1. Find, to 3 significant figures, the magnitude of \(\mathbf { F }\).
2. Find, in degrees to 1 decimal place, the angle between the directions of \(\mathbf { F }\) and \(\mathbf { P }\).

3. \begin{figure}[h] \end{figure} Two forces \(\mathbf { P }\) and \(\mathbf { Q }\) act on a particle at a point \(O\). Force \(\mathbf { P }\) has magnitude 6 N and force \(\mathbf { Q }\) has magnitude 7 N . The angle between the line of action of \(\mathbf { P }\) and the line of action of \(\mathbf { Q }\) is \(120 ^ { \circ }\), as shown in Figure 1. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(\mathbf { R }\). Find

1. the magnitude of \(\mathbf { R }\),
2. the angle between the line of action of \(\mathbf { R }\) and the line of action of \(\mathbf { P }\).

7. \begin{figure}[h] \end{figure} Two forces, \(\mathbf { P }\) and \(\mathbf { Q }\), act on a particle. The force \(\mathbf { P }\) has magnitude 8 N and the force \(\mathbf { Q }\) has magnitude 5 N . The angle between the directions of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(50 ^ { \circ }\), as shown in Figure 3. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is the force \(\mathbf { R }\).

1. Find, to 3 significant figures, the magnitude of \(\mathbf { R }\).
2. Find, to the nearest degree, the size of the angle between the direction of \(\mathbf { P }\) and the direction of \(\mathbf { R }\).

2 Two horizontal forces of magnitudes 12 N and 19 N act at a point. Given that the angle between the two forces is \(60 ^ { \circ }\), calculate

1. the magnitude of the resultant force,
2. the angle between the resultant and the 12 N force.

Two forces, \(\mathbf{F}_1 = 3\mathbf{i} + 2\mathbf{j}\) newtons and \(\mathbf{F}_2 = \mathbf{i} - 3\mathbf{j}\) newtons, are added together to find a resultant force, \(\mathbf{R}\) newtons. This vector addition can be represented using a diagram. Identify the diagram below which correctly represents this vector addition. Tick (\(\checkmark\)) one box. [1 mark] \includegraphics{figure_14}