What are the values of a and b in this vector equation?

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To solve the vector equation a\vec{A} + b\vec{B} + \vec{C} = 0, where \vec{A} = (75, -60), \vec{B} = (-16, 60), and \vec{C} = (84, 16), one must set up a system of equations based on the components of the vectors. The discussion emphasizes the need to create two equations from the x and y components to find the values of a and b. The magnitude of the resultant vector is noted to be zero, indicating that the vectors must balance each other out. Participants suggest using methods for solving simultaneous equations, though the original poster expresses uncertainty about how to proceed. Understanding the process of solving these equations is crucial for determining the values of a and b.
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Let a\vec{A}+ b\vec{B} + \vec{C} = 0, where \vec{A} = (75, -60), \vec{B} = (-16, 60), and \vec{C} = (84,16). I need to find the value of a and b. I really have no idea where to start with this problem any help would be great!
 
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renncat2 said:
Let a\vec{A}+ b\vec{B} + \vec{C} = 0, where \vec{A} = (75, -60), \vec{B} = (-16, 60), and \vec{C} = (84,16). I need to find the value of a and b. I really have no idea where to start with this problem any help would be great!
Welcome to Physics Forums.

You have two equations, with two unknowns. How do you suppose you could solve them?
 
So far I found the magnitude of the resultant displacement. (Rx = 144, Ry = 16, \vec{R} = 144.886)
 
renncat2 said:
So far I found the magnitude of the resultant displacement. (Rx = 144, Ry = 16, \vec{R} = 144.886)
The magnitude of the resultant vector is zero, by definition.

How do you normally solve systems of simultaneous equations?
 
i don't know. can you give me an example?
 
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