Math Problem Statement
Given r ( t )
− 4 t 2 i + e − 2 t j + 4 t k and u ( t )
2 t 3 i + e − 9 t j + 3 t 3 k , calculate d d t [ r ( t ) × u ( t ) ] .
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Calculus
Cross Product
Derivative of Vector Functions
Formulas
Cross product: A × B = |i j k|
|A1 A2 A3|
|B1 B2 B3|
Derivative of vector functions: d/dt [A(t) × B(t)]
Theorems
Product Rule for Differentiation
Properties of Cross Product
Suitable Grade Level
Undergraduate - Calculus III
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