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p0262

# p0262 - 174 CHAPTER 2 PARTICLE KINEMATICS 2.62 Chapter 2...

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174 CHAPTER 2. PARTICLE KINEMATICS 2.62 Chapter 2, Problem 62 Problem: Consider the vectors A = x i + x 1 j and B = x i + x 2 j . Compute the first derivative of A × B with respect to x by forming the cross product and differentiating. Verify that the chain rule for a cross product [Equation (2.38)] yields the same derivative. Solution: The cross product of A and B is A × B = e e e e e e e i j k x x 1 0 x x 2 0 e e e e e e e = D x 3 1 i k Differentiation with respect to x yields d dx ( A × B ) = 3 x 2 k To check for consistency with the chain rule, note that
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