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Exercise 16

Avg difficulty 2.5
  1. If u⃗×w⃗=0⃗\vu \times \vw = \vzero, what does this say about the direction of u⃗\vu and w⃗\vw?

  2. Remember that the vector v⃗\vv has magnitude and direction, so the derivative dv⃗dt=a⃗\frac{d\vv}{dt} = \va will measure the change in both the magnitude and direction of of v⃗\vv. Write a few sentences to describe how if v⃗\vv and a⃗=dv⃗dt\va= \frac{d\vv}{dt} are in parallel directions, then the unit normal vector will be undefined at that point.

Long, Keller & Schlicker, Active Calculus Multivariable, §10.6 Curvature, Exercise 16

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Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.