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Problem 3: The equation ax + by + cz = 0 describes a plane in R that passes through the origin. The curve C in R is parameterized by r(t) = (-6sin(2t), 8 sin(2t), 10 cos(2t)) for 0

Problem 3: The equation ax + by + cz = 0 describes a plane in R that passes through the origin. The curve C in R is parameterized by r(t) = (-6sin(2t), 8 sin(2t), 10 cos(2t)) for 0

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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Problem 3: The equation ax + by + cz = 0 describes a plane in R that passes through the origin. The curve C in R° is parameterized by r(t) = (-6 sin(2t), 8 sin(2t), 10 cos(2t)) for 0 <t < T. Find all points (x, y, z) in R³ where the curve C intersects the plane x + 2y – z = 0. Explain your work; solutions with insufficient or unclear explanations will be penalized. А. Recall that The equation ax + by + cz = 0 describes a plane in R3 that passes through the origin. The curve C in R³ is parameterized by r (t) = (-6 sin(2t), 8 sin(2t), 10 cos(2t)) for 0 <t<a. В. Find specific values for a, b, and c - not all of which are 0 - so the curve traced out by r (t) lies on the plane ax + by + cz = 0 or state that no such scalars exist. Explain your work; solutions with insufficient or unclear explanations will be penalized.
Transcribed Image Text:Problem 3: The equation ax + by + cz = 0 describes a plane in R that passes through the origin. The curve C in R° is parameterized by r(t) = (-6 sin(2t), 8 sin(2t), 10 cos(2t)) for 0 <t < T. Find all points (x, y, z) in R³ where the curve C intersects the plane x + 2y – z = 0. Explain your work; solutions with insufficient or unclear explanations will be penalized. А. Recall that The equation ax + by + cz = 0 describes a plane in R3 that passes through the origin. The curve C in R³ is parameterized by r (t) = (-6 sin(2t), 8 sin(2t), 10 cos(2t)) for 0 <t<a. В. Find specific values for a, b, and c - not all of which are 0 - so the curve traced out by r (t) lies on the plane ax + by + cz = 0 or state that no such scalars exist. Explain your work; solutions with insufficient or unclear explanations will be penalized.
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