# Calculus

a) Prove that |A|^2 = A•A for every vector A. (Note, the A's are vectors)

b)Use this to show that if |F(t)| is constant for t for all (a,b), then F'(t)•F(t) = 0 for t for all (a,b). (Note the Fs are vectors)

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1. (a) Since the definition of a dot product of A and B vectors , where A and B are vectors, is |A| |B| cos theta, then if B = A, then the angle between the two vectors is zero and {A}^2 = A*A

(b) What are a and b? You don't define them.

If the magnitude of F is constant, the vector F can only change in direction. The change in F is then perpendicular to F, and the dot product of the rate of change with F is zero.

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posted by drwls

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