Explanation Given info. r 1 ( t ) = 〈 t 2 , 1 , 2 t 〉 r 2 ( t ) = 〈 1 , 2 , e t 〉 Formula used: 〈 a 1 , b 1 , c 1 〉 . 〈 a 2 , b 2 , c 2 〉 = 〈 a 1 a 2 , b 1 b 2 , c 1 c 2 〉 (Dot product of two vector ) Calculation: 〈 t 2 , 1 , 2 t 〉 〈 1 , 2 , e t 〉 = 〈 t 2 , 2 , 2 t e t 〉 r 1 ( t ) . r 2 ( t ) = 〈 t 2 , 2 , 2 t e t 〉 = t 2 + 2 + 2 t e t Now Differentiate r 1 ( t ) . r 2 ( t ) w.r.t t d d t [ r 1 ( t ) ... To determine (b) d d t r 1 ( t ) . r 2 ( t ) | t = 1 Using the product rule.

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.2, Problem 23E

To determine

(a)

$r_{1} (t) . r_{2} (t)$ And differentiate.

To determine

(b)

$\frac{d}{d t} r_{1} (t) . r_{2} (t) |_{t = 1}$ Using the product rule.

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Chapter 14.2, Problem 22E

Chapter 14.2, Problem 24E

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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(a) r 1 ( t ) . r 2 ( t ) And differentiate.

Solution Summary: The author explains how to determine r 1 (t ) and differentiate.

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(a)

$r_{1} (t) . r_{2} (t)$ And differentiate.

(b)

$\frac{d}{d t} r_{1} (t) . r_{2} (t) |_{t = 1}$ Using the product rule.

Want to see the full answer?

Chapter 14 Solutions

(a) r 1 ( t ) . r 2 ( t ) And differentiate.

Solution Summary: The author explains how to determine r 1 (t ) and differentiate.

Concept explainers

Videos

(a) r1(t).r2(t) And differentiate.

(b) ddtr1(t).r2(t)|t=1 Using the product rule.

Want to see the full answer?

Chapter 14 Solutions

(a)

$r_{1} (t) . r_{2} (t)$ And differentiate.

(b)

$\frac{d}{d t} r_{1} (t) . r_{2} (t) |_{t = 1}$ Using the product rule.