Equilibrium of Three Forces: Solving with Vectors?

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To determine the equilibrium of three forces acting on an object, a diagram is essential for visualizing the forces and their angles. The forces include a 60-N force, a 35-N force at 20 degrees relative to the 60-N force, and a 40-N force at 75 degrees relative to the 60-N force. The sine and cosine laws are applicable for resolving these forces into their vector components. The challenge lies in using vectors instead of coordinate angles, which requires breaking down the forces into their x and y components. Understanding how to apply vector addition will be crucial for solving the problem effectively.
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Homework Statement


Three forces at on an object. A 35-N force acts an angle of 20^o relative to a 60-N force. A 40-N force acts at an angle of 75^o relative to the 60-N force on the opposite side of the 35-N force. Determine the equilibrium of the three forces.

Force 1 = 60 N
Force 2 = 35 N
Force 3 = 40 N

Homework Equations


Sine law
Cosine law


The Attempt at a Solution



I have no idea how to do this because my teacher only taught me about the forces dealing with two forces acting on an object.
 
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Draw yourself a diagram. Choose a coordinator of 0,90,180,270 degrees. What ever force is not on the coordinator could be broken down into x and y component.
That is how I would do it.
 
that is how I would do it as well. However, my teacher will want vectors and not coordinators. How does one do it with vectors?
 

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