Answered: Let r(t) = cost i + e^t j + t^2 k be…

Let r(t) = cost i + e^t j + t^2 k be given. A) Find the unit tangent vector to the curve at any point. B) Write the parametric equation of the tangent line to the curve at (1,1,0).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 43E

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Let r(t) = cost i + e^t j + t^2 k be given.

A) Find the unit tangent vector to the curve at any point.

B) Write the parametric equation of the tangent line to the curve at (1,1,0).

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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