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

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 θ₁ cos θ₂, sin θ₂, with θ₁ and θ₂ as in Figure 29. Then use the addition formula for the cosine to show that

Transcribed Image Text:

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