Answer :
We are given three forces acting on an object at different angles with respect to the positive x-axis. We need to find the direction and magnitude of the resultant force. To solve this problem, we can use vector addition to find the sum of the forces, and then calculate the magnitude and direction of the resultant force.
To find the resultant force, we start by resolving each force into its x and y components. The x-component of a force F with an angle θ can be calculated as Fx = F * cos(θ), and the y-component can be calculated as Fy = F * sin(θ). By applying these formulas to each force, we can determine the x and y components of all three forces.
Next, we add up the x-components and y-components separately to find the total x-component (Rx) and total y-component (Ry) of the resultant force. Rx is the sum of the x-components of the three forces, and Ry is the sum of the y-components.
Finally, we can find the magnitude of the resultant force (R) using the formula R = sqrt(Rx^2 + Ry^2), and the direction (θ) using the formula θ = atan(Ry/Rx). The magnitude of the resultant force is the length of the vector formed by the components, and the direction is the angle it makes with the positive x-axis.
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