Two unit vectors, a 1 and a 2 , lie in the x y plane and pass
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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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