Chapter 1: Vectors, Lines and Planes
Section 1.3: Dot Product
If A and B are unit vectors with θ the angle between them, show that sinθ/2=12A−B.
To establish the given identity, begin by squaring both sides. The left side then yields to the half-angle formula for the sine; the right side contains the square of the norm of the difference, which then becomes the dot product of the difference with itself. Each time the norm of A or B appears, remember that these are unit vectors, so the norms are 1.
=1− A B cos(θ)2
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