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(φ1 − φ2) = cos φ1 cos φ2 + sin φ1 sin φ2; (c) take the cross product and verify the trigonometric identity sin(φ2 − φ1) = sin φ2 cos φ1 − cos φ2 sin φ1.
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