p0245 - 2.45 CHAPTER 2 PROBLEM 45 129 2.45 Chapter 2...

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2.45. CHAPTER 2, PROBLEM 45 129 2.45 Chapter 2, Problem 45 Problem: Consider the vectors A = t i +2 t 2 j t k and B = i + t j + t 2 k . Compute the first derivative of A · B with respect to time by forming the dot product and differentiating. Verify that the chain rule for a dot product [Equation (2.37)] yields the same derivative. Solution: The dot product of A and B is A · B = t t 3 t 3 = t + t 3 Differentiation with respect to t yields d dt ( A · B )=1+3 t 2 To check for consistency with the chain rule, note that
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