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burhan101

  • 2 years ago

Are these planes parallel and distinct or parallel and coincident ? 3x+9y-6z-24=0 4x+6y-14z-8=0

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  1. tkhunny
    • 2 years ago
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    Divide the first by 3 and the second by 2, for starters.

  2. burhan101
    • 2 years ago
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    @tkhunny and then ??

  3. tkhunny
    • 2 years ago
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    What do you get?

  4. burhan101
    • 2 years ago
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    x=4+5z

  5. tkhunny
    • 2 years ago
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    ?? What is that? I was hoping you would get: x+3y-2z-8=0 2x+3y-7z-4=0

  6. burhan101
    • 2 years ago
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    Yes i did

  7. burhan101
    • 2 years ago
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    Then i did elimination to get rid of y

  8. tkhunny
    • 2 years ago
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    Why? Are they parallel?

  9. burhan101
    • 2 years ago
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    Yes

  10. burhan101
    • 2 years ago
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    We have to figure of if theyre parallel and distinct or coincidentt

  11. tkhunny
    • 2 years ago
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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?

  12. burhan101
    • 2 years ago
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    its given in the question

  13. tkhunny
    • 2 years ago
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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?

  14. burhan101
    • 2 years ago
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    so they're not parallel, they intersect ?

  15. tkhunny
    • 2 years ago
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    That's what they look like to me.

  16. burhan101
    • 2 years ago
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    Answer key says parallel and coincident

  17. tkhunny
    • 2 years ago
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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.

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