Explanation Given info : r 1 → ( t ) = ( t , t 2 , e t ) r 2 → ( t ) = ( e t , t 2 , t ) r 3 → ( t ) = ( t , t 2 , Cos t ) Concept used: Projection of general points ( x , y , z ) on the x y plane is given by ( x , y , 0 ) Calculation: r 1 → ( t ) = ( t , t 2 , e t ) x = t , y = t 2 , z = e t Hence co-ordinate of points on the space curve r 1 → ( t ) is ( t , t 2 , e t ) Projection of these points on the x y plane is ( t , t 2 , 0 )

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ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 14.1, Problem 16E

To determine

Which of the following curve have the same projection on the $x y$ plane?

(a) $\vec{r_{1}} (t) = (t, t^{2}, e^{t})$

(b) $\vec{r_{2}} (t) = (e^{t}, t^{2}, t)$

(c) $\vec{r_{3}} (t) = (t, t^{2}, Cos t)$

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Chapter 14.1, Problem 15E

Chapter 14.1, Problem 17E

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Chapter 14 Solutions

EBK CALCULUS

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 curve have the same projection on the x y plane? (a) r 1 → ( t ) = ( t , t 2 , e t ) (b) r 2 → ( t ) = ( e t , t 2 , t ) (c) r 3 → ( t ) = ( t , t 2 , Cos t )

Solution Summary: The author determines which of the following curves have the same projection on the x y plane.

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Which of the following curve have the same projection on the $x y$ plane?

(a) $\vec{r_{1}} (t) = (t, t^{2}, e^{t})$

(b) $\vec{r_{2}} (t) = (e^{t}, t^{2}, t)$

(c) $\vec{r_{3}} (t) = (t, t^{2}, Cos t)$

Want to see the full answer?

Chapter 14 Solutions

Which of the following curve have the same projection on the x y plane? (a) r 1 → ( t ) = ( t , t 2 , e t ) (b) r 2 → ( t ) = ( e t , t 2 , t ) (c) r 3 → ( t ) = ( t , t 2 , Cos t )

Solution Summary: The author determines which of the following curves have the same projection on the x y plane.

Videos

Which of the following curve have the same projection on the xy plane? (a) r1→(t)=(t,t2,et) (b) r2→(t)=(et,t2,t) (c) r3→(t)=(t,t2,Cost)

Want to see the full answer?

Chapter 14 Solutions

Which of the following curve have the same projection on the $x y$ plane?

(a) $\vec{r_{1}} (t) = (t, t^{2}, e^{t})$

(b) $\vec{r_{2}} (t) = (e^{t}, t^{2}, t)$

(c) $\vec{r_{3}} (t) = (t, t^{2}, Cos t)$