This exercise gives another proof of the relation between the dot product and the angle between two vectors v = (a 1 , b

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

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