Chapter 11: Q. 9 (page 900)

$Give precise mathematical definitions or descriptions of each of the concepts that follow . Then illustrate the definition with a graph or an algebraic example . the principal unit normal vector at r (t)$

Short Answer

Expert verified

$N (t) = \frac{T' (t)}{||T' (t)||}$

Step by step solution

Step 1. Given information is:

A differentiable vector function r(t)

Step 2. Principal Unit Normal Vector

$Let r (t) be a differentiable vector function on some interval I \subseteq ℝ such that the derivative of the unit tangent vector T' (t) \neq 0 on I . The principal unit normal vector at r (t) is defined to be : N (t) = \frac{T' (t)}{||T' (t)||} .$

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$Give precise mathematical definitions or descriptions of each of the concepts that follow . Then illustrate the definition with a graph or an algebraic example . the principal unit normal vector at r (t)$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Principal Unit Normal Vector

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Giveprecisemathematicaldefinitionsordescriptionsofeachoftheconceptsthatfollow.Thenillustratethedefinitionwithagraphoranalgebraicexample.theprincipalunitnormalvectoratr(t)

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Principal Unit Normal Vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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$Give precise mathematical definitions or descriptions of each of the concepts that follow . Then illustrate the definition with a graph or an algebraic example . the principal unit normal vector at r (t)$