Find Vector B Magnitude & Angle Given Vector A & (a+b)

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To find the magnitude and angle of vector B given vector A and the magnitude of vector (a+b), additional information is required. Without knowing the angle between vectors A and B, the solution remains indeterminate. A vector triangle can be drawn, but it only provides a locus of possible positions for vector B, forming a circle around the base of vector A. If the angle between A and B is known, it still does not yield a unique solution due to the circular locus constraint. Therefore, more data is essential to determine a definitive result for vector B.
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if you know the magnitude and angle of vector A and you are given the magnitude of vector (a+b) how would you go about find the mag and angle for vector b
 
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You can't. Draw a vector triangle. If you knew the angle BETWEEN A and B and the other information, you would have a SAS triangle situation and this could be solved. If you only have the direction of A (the angle, as you put it), the solution is indeterminant.
 
2slowtogofast said:
if you know the magnitude and angle of vector A and you are given the magnitude of vector (a+b) how would you go about find the mag and angle for vector b

Looked at another way, the locus of the end of the result vector describes a circle about the base of the Vector A whose radius is the magnitude. You need some additional piece of information to determine a unique result vector.

Edit: The previous description presumes the angle of A is with the coordinate system. Now if you know the angle between A and B, if that is the statement of the problem, then you still don't have sufficient information because all you may know then is the intersection along that direction with the circular locus of the magnitude.
 
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