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# Vector A has a magnitude of 8.00 units and makes an angle of $$45.0^\circ$$ with the positive x-axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x-axis. Find (a) the vector sum A + B and (b) the vector sum of A-B?

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#### AnswerA + B = 6,123 units at angle 112,5 degrees.A - B = 14,782 units at angle 22,5 degrees.Explanation:For vector addition, we resolve each vector into horizontal and vertical components and then add each direction separately. The overall magnitude is ten found from Pythagoras, and the direction from a trig ratio. (Details in sketch)For vector subtraction, simply add the negative of the second vector and repeat the process.

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