Explanation Given information: r ( t ) = 〈 4 t , 5 t , 9 t 〉 , t = − 4 Concept used: Parametrization of tangent line is given by l ( t ) = r ( a ) + t r ' ( a ) . Where, r ( t ) is given by 〈 x ( t ) , y ( t ) , z ( t ) 〉 , t = a and r ' ( t ) = 〈 d d t x ( t ) , d d t y ( t ) , d d t z ( t ) 〉 ( componentwise differentiation ) Calculation: Parametrization of tangent line at t = − 4 is l ( t ) = r ( − 4 ) + t r ' ( − 4 ) . ...... ( 1 ) Now, find the value r ( − 4 ) . r ( − 4 ) = 〈 4 ( − 4 ) , 5 ( − 4 ) , 9 ( − 4 ) 〉 r ( − 4 ) = 〈 − 16 , − 20 , − 36 〉

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 14.2, Problem 32E

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The parametrization of tangent line to r(t)=〈4t,5t,9t〉 at the point t=−4.

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Chapter 14.2, Problem 31E

Chapter 14.2, Problem 33E

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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 parametrization of tangent line to r ( t ) = 〈 4 t , 5 t , 9 t 〉 at the point t = − 4 .

Solution Summary: The author explains the parametrization of tangent line to r(t)=langle -16+4t,-20+5t

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The parametrization of tangent line to r(t)=〈4t,5t,9t〉 at the point t=−4.

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