Calculating Y-Component of Vector B: Solve Vectors Question

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To calculate the y-component of vector B, the relationship between vectors A and B must be understood, particularly that vector A minus vector B is parallel to the -x axis. This implies that the y-components of A and B must be equal in magnitude but opposite in direction. The formula for the y-component of vector B, By = Bcos(theta), requires knowing the magnitude of vector B, which is not provided. The key to solving the problem lies in recognizing that the angles and the relationship between the vectors can help deduce the necessary information about vector B. Understanding this relationship is crucial for proceeding with the calculations.
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Homework Statement


The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated.
DATA: α= 47.5o β= 56.6o |A| = 7.9 cm. The vector A - B is parallel to the -x axis (points due West). Calculate the y-component of vector B.

Homework Equations


By=Bcos(theta)


The Attempt at a Solution


I haven't attempted this yet. What I need help with is setting it up, not actually solving the problem. I feel like some data is missing. In order for me to calculate the y component using the formula listed above, I need to know B. But I am only given A. So how do I find B? I can't find it anywhere. There are other parts to this question but I think I can handle those once I get B. Can someone help me figure out what I am missing here? Thanks :)
 
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Think about it like an algebra problem, instead of giving you A and B and asking you to find the result (lets call it C), they're giving you A, and telling you something important about the resultant (C)---i.e. note that they say A-B is parallel to the -x axis, what does that tell you?
How can you use that information?
 

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