Problem

Two unit vectors, a1 and a2, lie in the xy plane and pass through the origin. They make an...

Two unit vectors, a1 and a2, lie in the xy plane and pass through the origin. They make angles ϕ1 and ϕ2, respectively, with the x axis (a) Express each vector in rectangular components; (b) take the dot product and verify the trigonometric identity, cos(ϕ1ϕ2) = cos ϕ1 cos ϕ2 + sin ϕ1 sin ϕ2; (c) take the cross product and verify the trigonometric identity sin(ϕ2ϕ1) = sin ϕ2 cos ϕ1 − cos ϕ2 sin ϕ1.

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Solutions For Problems in Chapter 1