(a) Explanation Given: A parametric curve r ( t ) = 〈 t cos t , t sin t , t 〉 . Calculation: In order to show that the given parametric curve lies on the cone x 2 + y 2 = z 2 , we will plug r ( t ) = 〈 t cos t , t sin t , t 〉 in the cone x 2 + y 2 = z 2 ... (b) To determine To sketch: The given parametric curve r ( t ) = 〈 t cos t , t sin t , t 〉 and the cone x 2 + y 2 = z 2 .

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 14.1, Problem 25E

(a)

To determine

To show:

That the given parametric curve lies on the cone $x^{2} + y^{2} = z^{2}$ .

(b)

To determine

To sketch:

The given parametric curve $r (t) = 〈 t \cos t, t \sin t, t 〉$ and the cone $x^{2} + y^{2} = z^{2}$ .

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Chapter 14.1, Problem 24E

Chapter 14.1, Problem 26E

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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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That the given parametric curve lies on the cone x 2 + y 2 = z 2 .

Solution Summary: The author illustrates how the parametric curve lies on the cone x 2 + y 2 = z 2.

Concept explainers

To show:

That the given parametric curve lies on the cone $x^{2} + y^{2} = z^{2}$ .

To sketch:

The given parametric curve $r (t) = 〈 t \cos t, t \sin t, t 〉$ and the cone $x^{2} + y^{2} = z^{2}$ .

Want to see the full answer?

Chapter 14 Solutions

That the given parametric curve lies on the cone x 2 + y 2 = z 2 .

Solution Summary: The author illustrates how the parametric curve lies on the cone x 2 + y 2 = z 2.

Concept explainers

To show: That the given parametric curve lies on the cone x2+y2=z2.

To sketch: The given parametric curve r(t)=〈tcost,tsint,t〉 and the cone x2+y2=z2.

Want to see the full answer?

Chapter 14 Solutions

To show:

That the given parametric curve lies on the cone $x^{2} + y^{2} = z^{2}$ .

To sketch:

The given parametric curve $r (t) = 〈 t \cos t, t \sin t, t 〉$ and the cone $x^{2} + y^{2} = z^{2}$ .