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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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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