Explanation Calculation: Refer to Figure 12.15 in the textbook. The velocity vector v = d r ( t ) d t is tangent to the curve r ( t ) and a differential curve’s unit tangent vector can be expressed as follows, T = v | v | (1) Here, v is the velocity vector. T is the differential function of t whenever v is the differential function of t . For example: Consider the curve r ( t ) = ( 1 + 2 cos t ) i + ( 2 sin t ) j + t 2 k representing the path of a hang glider. Find the unit tangent vector. The velocity vector is, v = d r ( t ) d t (2) Substitute ( 1 + 2 cos t ) i + ( 2 sin t ) j + t 2 k for r ( t ) in equation (2) to find the velocity vector v . v = d d t [ ( 1 + 2 cos t ) i + ( 2 sin t ) j + t 2 k ] v = − ( 2 sin t ) i + ( 2

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ISBN: 9781323835029

Author: WEIR

Publisher: PEARSON C

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Chapter 13, Problem 7GYR

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Explain a differential curve’s unit tangent vector is explained with an example.

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