Vector A has a magnitude of 8.00 units and makes an angle of 45.0° 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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Sep 3, 2015


A + B = 6,123 units at angle 112,5 degrees.
A - B = 14,782 units at angle 22,5 degrees.


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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