Explanation Given info. Given statements (a) If r → 1 ( t ) and r → 2 ( t ) intersect, then they collide. (b) If r → 1 ( t ) and r → 2 ( t ) collide, then they intersect. (c) Intersection depends only on the underlying curves traced by r → 1 ( t ) and r → 2 ( t ) , but collision depends on the actual parameterizations. Concept used: Two path r → 1 ( t ) and r → 2 ( t ) intersect if there is a point p lying on both curve. i.e. r → 1 ( t 1 ) = r → 2 ( t 2 ) , but t 1 may not be equal to t 2 . Two path r → 1 ( t ) and r → 2 ( t ) intersect if r → 1 ( t 1 ) = r → 2 ( t 2 ) and t 1 = t 2 ...

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14.1, Problem 36E

To determine

Which of the following statements are true?

(a) If ${\vec{r}}_{1} (t) and {\vec{r}}_{2} (t)$ intersect, then they collide.

(b) If ${\vec{r}}_{1} (t) and {\vec{r}}_{2} (t)$ collide then they intersect.

(c) Intersection depends only on the underlying curves traced by ${\vec{r}}_{1}$ and ${\vec{r}}_{2}$ but collision depends on the actual parameterizations.

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Chapter 14.1, Problem 35E

Chapter 14.1, Problem 37E

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Chapter 14 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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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Which of the following statements are true? (a) If r→1(t) and r→2(t) intersect, then they collide. (b) If r→1(t) and r→2(t) collide then they intersect. (c) Intersection depends only on the underlying curves traced by r→1 and r→2 but collision depends on the actual parameterizations.

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Chapter 14 Solutions