(a) To determine Find the value of the unit normal vector for the given curve. Explanation Given data: The expression of the curve is, r ( t ) = t i + 1 3 t 3 j (1) Formula used: Write a general expression to calculate constant vector v . v = d r d t (2) Here, d r d t is the value of change in plane curve. Write a general expression to calculate the principal unit normal vector. N = n | n | (3) Calculation: Substitute the equation (1) in equation (2) to find v . v = d d t ( t i + 1 3 t 3 j ) = ( 1 ) i + 1 3 ( 3 t 2 ) ( 1 ) j = i + t 2 j Given that either n or − n vector points towards the concave side of the curve and make it into a unit vector. Therefore, the vector n = t 2 i − j points towards the concave side of the curve when t < 0 and − n = − t 2 i + j points towards the concave side of the curve when t > 0 . Substitute t 2 i − j for n for t < 0 in equation (3) to find N (b) To determine Find the value of the unit normal vector for the given curve at t ≠ 0 .

Pearson eText for Thomas' Calculus: Early Transcendentals -- Instant Access (Pearson+)

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ISBN: 9780137399185

Author: Joel Hass, Christopher Heil

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Chapter 13.4, Problem 8E

(a)

To determine

Find the value of the unit normal vector for the given curve.

(b)

To determine

Find the value of the unit normal vector for the given curve at t≠0.

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Chapter 13.4, Problem 7E

Chapter 13.4, Problem 9E

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Chapter 13 Solutions

Pearson eText for Thomas' Calculus: Early Transcendentals -- Instant Access (Pearson+)

Ch. 13.1 - In Exercises 1–4, find the given limits. 1. Ch. 13.1 - In Exercises 1–4, find the given limits. 2. Ch. 13.1 - In Exercises 1–4, find the given limits. 3. Ch. 13.1 - In Exercises 1–4, find the given limits. 4. Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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