part b HW Problem 3: One way to try to determine the line of intersection of two planes in 3-space isto find two points of intersection. Once you have two points, the line throughthem must be the line of intersection. To find two such points, it may help tosearch for points that are in both planes and have one of the coordinates x, y, or zequal to zero.(a) Explain the geometric idea behind this method. (Visualize and think...)(b) Use this method to find the line of intersection of the plane x + 2y + 3z =and the plane x + y + z = 3. Express the line of intersection using parametricequations.(c) If two planes intersect, is it guaranteed that the method of setting one of thevariables equal to zero to find a point of intersection always find at least twopoints at which the planes intersect? Explain.Hint: What, geometrically, does it mean when you set x = 0, y = 0, or z = 0?

Answered: Image /qna-images/answer/6296ed2b-fc17-4275-8d39-c093ce55525f.jpg

Answered: Use this method to find the line of…

Use this method to find the line of intersection of the plane x + 2y + 3z = 6 and the plane x + y + z = 3. Express the line of intersection using parametric equations. %3D %3D

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 44E: By definition, a hyperbola is the locus of points whose positive difference of distances from two...

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Question

part b

HW Problem 3: One way to try to determine the line of intersection of two planes in 3-space is
to find two points of intersection. Once you have two points, the line through
them must be the line of intersection. To find two such points, it may help to
search for points that are in both planes and have one of the coordinates x, y, or z
equal to zero.
(a) Explain the geometric idea behind this method. (Visualize and think...)
(b) Use this method to find the line of intersection of the plane x + 2y + 3z =
and the plane x + y + z = 3. Express the line of intersection using parametric
equations.
(c) If two planes intersect, is it guaranteed that the method of setting one of the
variables equal to zero to find a point of intersection always find at least two
points at which the planes intersect? Explain.
Hint: What, geometrically, does it mean when you set x = 0, y = 0, or z = 0?

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