burhan101
Are these planes parallel and distinct or parallel and coincident ?
3x+9y-6z-24=0
4x+6y-14z-8=0
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tkhunny
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Divide the first by 3 and the second by 2, for starters.
burhan101
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@tkhunny and then ??
tkhunny
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What do you get?
burhan101
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x=4+5z
tkhunny
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?? What is that? I was hoping you would get:
x+3y-2z-8=0
2x+3y-7z-4=0
burhan101
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Yes i did
burhan101
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Then i did elimination to get rid of y
tkhunny
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Why? Are they parallel?
burhan101
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Yes
burhan101
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We have to figure of if theyre parallel and distinct or coincidentt
tkhunny
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They are? What makes you think so? When you eliminated y, didn't that give you a line in the x-z plane?
burhan101
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its given in the question
tkhunny
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Are you going to buy it, just because it says so? If they are parallel, shouldn't they have the same Normal Vector?
burhan101
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so they're not parallel, they intersect ?
tkhunny
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That's what they look like to me.
burhan101
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Answer key says parallel and coincident
tkhunny
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3x+9y-6z-24=0
4x+6y-14z-8=0
Find a point on one of them.
(10,0,1) Prove 3(10) + 9(0) - 6(1) - 24 = 30 + 0 - 6 - 24 = 24 - 24 = 0
Is it on the other one?
4(10) + 6(0) - 14(1) - 8 = 40 - 14 - 8 = 26 - 8 = 18 \(\ne 0\)
Okay, we just proved that they are NOT coincident.
Did you write the problem correctly? If you did, we're done.