Three forces act on a bracket: $F_1 = 100\text{ N}$ at $30^\circ$, $F_2 = 150\text{ N}$ at $120^\circ$, and $F_3 = 200\text{ N}$ at $270^\circ$ (measured counter-clockwise from the positive x-axis). Determine the magnitude and direction of the resultant.

A force of $F = 400 \text{ N}$ acts on the end of a lever of length $L = 2 \text{ m}$ at an angle of $60^\circ$ to the lever. Calculate the moment of the force about the pivot point.

Two forces act on a point: $\mathbf{F}_1 = \{30\mathbf{i} + 40\mathbf{j} - 50\mathbf{k}\} \text{ N}$ and $\mathbf{F}_2 = \{-20\mathbf{i} + 10\mathbf{j} + 30\mathbf{k}\} \text{ N}$. Find the resultant force vector and its magnitude.

When a cable is used to pull a car out of a ditch, the force exerted by the winch is applied to the bumper of the car. According to the Principle of Transmissibility, we can treat this force as if it were applied anywhere along its line of action. Discuss why this is valid for the car as a whole, but not for the bumper itself.

When a driver turns a steering wheel using both hands, they apply equal and opposite forces on opposite sides of the wheel. Explain this action in terms of force systems and why it is an ideal way to turn the wheel.