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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04fb1644-6128-4051-bfd7-20e522232dc3%2F10cd271f-6bbe-4b51-a728-04287c58b876%2Fu4agzws_processed.png&w=3840&q=75)
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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