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Applications of the Dot Product (Vectors)

Determine the angle between vector PQ and the positive x-axis, given endpoints P(4,7) and Q (8,3)
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The angle will be measured in a way that positive is counterclockwise and negative is the complement to 180 degrees. so the tang of the angle will be (Y2 - Y1)/(X2-X1) = (3-7)/(8-4); then tang φ = -4/4 = -1 = -45 degrees buy measured from the positive side of the x axis, it will be 135 degrees.