7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
7.4 Intersecon of Three Planes
Case 1: The planes intersect at a point.
There is exactly one soluon.
parallel
Case 2: The planes intersect in a line.
There are an infinite # of soluons.
Requires the use of 1 parameter.
parallel
Two coincident
coincident planes.
Case 3: The planes intersect in a plane (coincident planes).
There are an infinite number of soluons.
Requires the use of 2 parameters.
parallel
May 19-5:08 PM
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7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
Inconsistent Systems (there is no soluon):
Case 4: The three planes are parallel and at least 2 are disnct.
parallel
Case 5: Two planes are parallel and disnct.
The third plane is not parallel to the other two.
parallel
Case 6: The planes intersect in pairs.
The pairs intersect in lines that are parallel and disnct.
parallel
May 19-5:09 PM
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7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
Summary
Jun 3-7:24 AM
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7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
Ex. 1
May 19-5:09 PM
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7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
x - 5y + 2z - 10 = 0
x + 7y - 2z + 6 = 0
May 19-5:11 PM
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7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
3x + y - 2z = 7
x - 5y + z = 8
12x + 4y - 8z = -4
May 19-5:12 PM
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7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
x + 3y - z = -10
2x + y + z = 8
x - 2y + 2z = -4
May 19-5:13 PM
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7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
4x - 2y + 6z = 35
6x - 3y + 9z = -50
May 19-5:14 PM
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7.4 Intersection of 3 planesNEW.notebook
June 03, 2016
Homework
Page 531
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