4. Consider the vector function v(t) = (t, t², t³). (a) (10 points) Find the unit tangent vector function T(t), the unit normal vector function N(t), and the binormal vector function B(t). (b) (5 points) Give an equation for the normal plane to v in terms of t. (c) (10 points) Find the curvature к and the torsion 7 in terms of t.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4. Consider the vector function v(t) = (t, t², t³).
(a) (10 points) Find the unit tangent vector function T(t), the unit normal vector function N(t), and
the binormal vector function B(t).
(b) (5 points) Give an equation for the normal plane to v in terms of t.
(c) (10 points) Find the curvature к and the torsion 7 in terms of t.
Transcribed Image Text:4. Consider the vector function v(t) = (t, t², t³). (a) (10 points) Find the unit tangent vector function T(t), the unit normal vector function N(t), and the binormal vector function B(t). (b) (5 points) Give an equation for the normal plane to v in terms of t. (c) (10 points) Find the curvature к and the torsion 7 in terms of t.
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