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A plane in R³ contains the point (-r, 0, 1) and has the vector (1,4,3r) as a normal, where r is a real number. (a) Determine the equation of the plane in terms of r. (b) Given that the point (0, -2, 2) also lies in the plane, determine the equation of the plane. (c) Find the point of intersection of the plane with the y-axis.

A plane in R³ contains the point (-r, 0, 1) and has the vector (1,4,3r) as a normal, where r is a real number. (a) Determine the equation of the plane in terms of r. (b) Given that the point (0, -2, 2) also lies in the plane, determine the equation of the plane. (c) Find the point of intersection of the plane with the y-axis.

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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A plane in R³ contains the point (-r, 0, 1) and has the vector (1,4,3r) as a normal, where r is a real number. (a) Determine the equation of the plane in terms of r. (b) Given that the point (0, -2, 2) also lies in the plane, determine the equation of the plane. (c) Find the point of intersection of the plane with the y-axis.
Transcribed Image Text:A plane in R³ contains the point (-r, 0, 1) and has the vector (1,4,3r) as a normal, where r is a real number. (a) Determine the equation of the plane in terms of r. (b) Given that the point (0, -2, 2) also lies in the plane, determine the equation of the plane. (c) Find the point of intersection of the plane with the y-axis.
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