Need help with Problem 2. Thank you :) Problem 1. Let L be the line (t + 1, 2t, 3t – 1), t e R, and A the point (1, 1, 1). Let P bethe plane containing L and A.(a) Write down a normal vector to P.(b) Write down an algebraic and a parametric equation for P.Problem 2. Consider the space curve 7(t) = (eat, e2at, e3at) for a postitive constant a > 0.(a) Find the point where the space curve intersects the plane P from Problem 1.(b) Find all values of a such that the space curve is tangential to the plane P.

Given the space curve r→t=eαt,e2αt,e3αt, α>0. The equation of the plane obtained in problem 1 is…

Problem 2. Consider the space curve 7(t) = (et, e2at, e3at) for a postitive constant a > 0. (a) Find the point where the space curve intersects the plane P from Problem 1. (b) Find all values of a such that the space curve is tangential to the plane P.

Problem 2. Consider the space curve 7(t) = (et, e2at, e3at) for a postitive constant a > 0. (a) Find the point where the space curve intersects the plane P from Problem 1. (b) Find all values of a such that the space curve is tangential to the plane P.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 35E

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Need help with Problem 2. Thank you :)

Problem 1. Let L be the line (t + 1, 2t, 3t – 1), t e R, and A the point (1, 1, 1). Let P be
the plane containing L and A.
(a) Write down a normal vector to P.
(b) Write down an algebraic and a parametric equation for P.
Problem 2. Consider the space curve 7(t) = (eat, e2at, e3at) for a postitive constant a > 0.
(a) Find the point where the space curve intersects the plane P from Problem 1.
(b) Find all values of a such that the space curve is tangential to the plane P.

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