Explanation Given: r ( θ ) = R 〈 cos θ , sin θ 〉 , the circle of radius R The equation of normal vector, N ( θ ) = T ' ( θ ) | T ' ( θ ) | Where, T ( θ ) = r ' ( θ ) | r ' ( θ ) | Where, r ( θ ) = R 〈 cos θ , sin θ 〉 First find the derivative of r i r ' ( θ ) = R 〈 − sin θ , cos θ 〉 | r ' ( θ ) | = R sin 2 θ + cos 2 θ | r ' ( θ ) | = R Substitute the value into T ( θ ) = r ' ( θ ) | r ' ( θ ) | T ( θ ) = R 〈 − sin θ , cos θ 〉 R T

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Author: Rogawski

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Chapter 14.4, Problem 36E

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To find: The equation of normal vector N(θ) to r(θ) .

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Chapter 14.4, Problem 35E

Chapter 14.4, Problem 37E

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Chapter 14 Solutions

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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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The equation of normal vector N ( θ ) to r ( θ ) .

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To find: The equation of normal vector N(θ) to r(θ) .

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Chapter 14 Solutions