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Consider the points P = (3,2, –1), Q = (-1,1,1), and R= (-3,0,2). %3D (a) Find parametric and cartesian equations for the plane P1 that goes through the three points. (b) Find cartesian equations for the plane P2 that goes through the point P and is perpendicular to both Pi and to the plane with equation x – 4y + 2z = 4. (Hint: the perpendicularity condition means that a normal vector to P2 needs to be orthogonal to both a normal vector of Pi and to a normal vector of the plane with equation x – 4y + 2z = 4. And you do know how to find a vector that is orthogonal to two other vectors.) 2.

Consider the points P = (3,2, –1), Q = (-1,1,1), and R= (-3,0,2). %3D (a) Find parametric and cartesian equations for the plane P1 that goes through the three points. (b) Find cartesian equations for the plane P2 that goes through the point P and is perpendicular to both Pi and to the plane with equation x – 4y + 2z = 4. (Hint: the perpendicularity condition means that a normal vector to P2 needs to be orthogonal to both a normal vector of Pi and to a normal vector of the plane with equation x – 4y + 2z = 4. And you do know how to find a vector that is orthogonal to two other vectors.) 2.

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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2. Consider the points P = (3, 2, –1), Q = (-1,1,1), and R= (-3,0,2). (a) Find parametric and cartesian equations for the plane Pi that goes through the three points. (b) Find cartesian equations for the plane P2 that goes through the point P and is perpendicular to both Pi and to the plane with equation x – 4y + 2z = 4. (Hint: the perpendicularity condition means that a normal vector to P2 needs to be orthogonal to both a normal vector of P1 and to a normal vector of the plane with equation x that is orthogonal to two other vectors.) 4y + 2z = 4. And you do know how to find a vector
Transcribed Image Text:2. Consider the points P = (3, 2, –1), Q = (-1,1,1), and R= (-3,0,2). (a) Find parametric and cartesian equations for the plane Pi that goes through the three points. (b) Find cartesian equations for the plane P2 that goes through the point P and is perpendicular to both Pi and to the plane with equation x – 4y + 2z = 4. (Hint: the perpendicularity condition means that a normal vector to P2 needs to be orthogonal to both a normal vector of P1 and to a normal vector of the plane with equation x that is orthogonal to two other vectors.) 4y + 2z = 4. And you do know how to find a vector
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