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Dot Product from the magnitudes of the vectors and the angle between them:

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Find ,

where |a| = 5 and |b| = 2 and the angle q between them is 150 degrees.

In this case the Dot Product is the product of the magnitudes and the cosine of the angle between them:

s = |a| * |b| * cos q . Here this becomes

s = 5 * 2 * cos(150) = 10 * (-.866) = -8.66.