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September 30th, 2010, 06:27 PM   #1
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Intersection of two planes in R3

I thought I understood equations of planes in R3 and their intersections, but apparently not. I'm very confused by what seems to be a basic problem:

find a vector equation for the line of intersection of x + y + z= 0 and x + z = 0.

Is x + z= 0 still a plane even though it doesn't have the form Ax + By + Cz = D?

I notice that if you set the two equations equal to each other you find that y = 1. Does this mean that the planes intersect on a line where y =1 and all x coordinates are equal to negative z coordinates? Thanks!
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October 2nd, 2010, 10:18 AM   #2
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Re: Intersection of two planes in R3

Hello, majami!

Quote:
Find a vector equation for the line of intersection of

Is still a plane even though it doesn't have the form ?[color=beige] . [/color][color=blue]Yes, it does.[/color]
[color=beige]. . [/color][color=blue]It has: A = 1, B = 0, C = 1, D = 0[/color]













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