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Angle between Vectors

We need a convenient way of describing the direction as well as the magnitude of a vector. First we define the angle between two vectors (Figure 10.1.20).


Figure 10.1.20


Let A and B be two nonzero vectors in the plane, and let 0 be the origin.

The angle between A and B is either the angle A0B or the angle B0A, whichever is in the interval [0, π]. (The angle between A and the zero vector is undefined.)

Notice that if A0B is between 0 and π, then B0A is between π and 2π, and vice versa. So exactly one is between 0 and π. The angle θ between A and B can be computed by using the Law of Cosines from trigonometry, illustrated in Figure 10.1.21.


Figure 10.1.21

Last Update: 2006-11-07