Given a Vector addition and subtraction, how to find the Vector.

AI Thread Summary
To solve for vectors A and B given the equations A+B = x1i + y1j and A-B = x2i + y2j, one effective method is to add the two equations. This results in 2A = (x1 + x2)i + (y1 + y2)j, allowing for the calculation of vector A as A = 0.5[(x1 + x2)i + (y1 + y2)j]. Similarly, subtracting the second equation from the first yields 2B = (x1 - x2)i + (y1 - y2)j, leading to B = 0.5[(x1 - x2)i + (y1 - y2)j]. This approach simplifies the problem and provides clear solutions for both vectors A and B.
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Homework Statement


Given the following Vectors: A+B= x1i + y1j and A-B= x2i + y2j
what is A? and what is B?

The Attempt at a Solution



I wasn't really sure how to go about this problem. I tried setting one side to A and pluging it into the other eqn A.. however that made no sense to me.
 
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That would work but try z1=A+B and z2=A-B, then what is z1+z2?
(do the A and B part as well as the i and j part)
 

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