Solving Vector Problems: Finding Magnitudes and Angles with A = 4

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To solve the vector problem where A = 4, the conditions state that the magnitude of the resultant vector from adding vectors A and B equals A, while subtracting them results in a magnitude of 2A. By applying the law of sines and cosines, as well as the component method, one can derive the value of vector B and the angle between the two vectors. The equations involve expanding dot products and utilizing the relationship A.B = |A||B|cos(theta). Ultimately, these calculations will yield the necessary values for B and the angle.
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I went through some old vector problems and did over 100 but I couldn't get my hands on this one, thanks for taking your time to help me out.


Problem: If vectors A and B are added, the resultant has magnitude A. If the two are subtracted, the resultant has a magnitude 2A. If A = 4 what is B and what is the angle between the two vectors.

Solve using triangles and the law of sinces/cosines, and also solve using the component approach.

Thanks much.
 
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If V is a vector with magnitude |V|, then V.V=|V|^2. So your first condition is (A+B).(A+B)=|A|^2. What's the second one? Expand out the dot products using the distributive property and solve for B.B and A.B. Then remember A.B=|A||B|cos(theta).
 

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