Explanation Given: r → ( t ) = 〈 t , 1 − t , t 2 〉 Formula used: T ∧ ( t ) = r ' → ( t ) ‖ r → ' ( t ) ‖ N ∧ ( t ) = T ∧ ' ( t ) ‖ T ∧ ' ( t ) ‖ Calculation: r → ( t ) = 〈 t , 1 − t , t 2 〉 r → ( t ) = d d t 〈 t , 1 − t , t 2 〉 ( differentiate both side ) or r → ( t ) = 〈 d t d t , d ( 1 − t ) d t , d t 2 d t 〉 = 〈 1 , − 1 , 2 t 〉 T ∧ ( t ) = r ' → ( t ) ‖ r → ' ( t ) ‖ = 〈 1 , − 1 , 2 t 〉 ‖ 〈 1 , − 1 , 2 t 〉 ‖ = 〈 1 , − 1 , 2 t 〉 ( 1 ) 2 + ( − 1 ) 2 + ( 2 t ) 2 ( ‖ 〈 a , b , c 〉 ‖ = a 2 + b 2 + c 2 ) = 〈 1 , − 1 , 2 t 〉 2 + 4 + 2 Hence T ∧ ( t ) = 〈 1 To determine (b) Find the general formula of B ∧ as function of t To determine (c) Nature of osculating plane. From result obtain from ( b ) part solution.

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ISBN: 9781319050733

Author: Rogawski

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Chapter 14.4, Problem 55E

To determine

(a)

Let $\vec{r} (t) = 〈 t, 1 - t, t^{2} 〉$

Find the general formula for $\overset{\land}{T} and \overset{\land}{N}$ as function of $\overset{\land}{t}$

To determine

(b)

Find the general formula of $\overset{\land}{B}$ as function of $t$

To determine

(c)

Nature of osculating plane. From result obtain from $(b)$ part solution.

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Chapter 14.4, Problem 54E

Chapter 14.4, Problem 56E

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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) Let r → ( t ) = 〈 t , 1 − t , t 2 〉 Find the general formula for T ∧ and N ∧ as function of t ∧

Solution Summary: The author explains how to determine the general formula for T and N as function of t.

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(a)

Let $\vec{r} (t) = 〈 t, 1 - t, t^{2} 〉$

Find the general formula for $\overset{\land}{T} and \overset{\land}{N}$ as function of $\overset{\land}{t}$

(b)

Find the general formula of $\overset{\land}{B}$ as function of $t$

(c)

Nature of osculating plane. From result obtain from $(b)$ part solution.

Want to see the full answer?

Chapter 14 Solutions

(a) Let r → ( t ) = 〈 t , 1 − t , t 2 〉 Find the general formula for T ∧ and N ∧ as function of t ∧

Solution Summary: The author explains how to determine the general formula for T and N as function of t.

Videos

(a) Let r→(t)=〈t,1−t,t2〉 Find the general formula for T∧ and N∧ as function of t∧

(b) Find the general formula of B∧ as function of t

(c) Nature of osculating plane. From result obtain from (b) part solution.

Want to see the full answer?

Chapter 14 Solutions

(a)

Let $\vec{r} (t) = 〈 t, 1 - t, t^{2} 〉$

Find the general formula for $\overset{\land}{T} and \overset{\land}{N}$ as function of $\overset{\land}{t}$

(b)

Find the general formula of $\overset{\land}{B}$ as function of $t$

(c)

Nature of osculating plane. From result obtain from $(b)$ part solution.