Multi Calc, Lec 3A: Position & Velocity Vectors, Speed, Distance (Arc Length) for Parametric Eqs

Multivariable Calculus, Lecture 3A

#MultivariableCalculus #ArcLength #PhysicsAndCalculus

Links and resources
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(0:00) Lissajous curve position vector, notation, and geometry
(4:47) i-hat and j-hat notation
(8:54) Sum vectors with parallelogram law
(11:20) Lissajous curve velocity vector (derivative of position vector) and geometric interpretation
(14:25) Magnitude of velocity vector is speed (use Pythagorean Theorem)
(16:34) Integral of speed is distance (arc length)
(17:52) Mathematica graphs and calculations for this example
(23:32) Integrals for arc length are often difficult

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