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

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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