This exercise gives another proof of the relation between the dot product and the angle between

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This exercise gives another proof of the relation between the dot product and the angle θ between two vectors v = (a1, b1) and w = (a2, b2) in the plane. Observe that v = ΙΙvΙΙ (cos θ1, sin θ1) and w = w θcos θ2, sin θ2, with θ1 and θas in Figure 29. Then use the addition formula for the cosine to show that

v. w = ||v||||w|| cos 0

021 W -X a1 0 V b -X W 0 0=0-01 X

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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