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IsTim

Which pairs of planes are parallel and distinct and which are conincident? 2x+4y-7z-2=0 4x+6y-14z-8=0

  • 2 years ago
  • 2 years ago

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  1. IsTim
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    I tried looking through my notes and textbook for this one, but unless there is a direct connection, I don't understand how to apply it to this question.

    • 2 years ago
  2. IsTim
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    I managed to answer some unrelated questions beforehand, but I don't know how I managed to solve them...

    • 2 years ago
  3. IsTim
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    So I figured out the normals were [2,3,7] and [4,6,-14]

    • 2 years ago
  4. IsTim
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    I can see that I just have to multiply 2,3,7 by 2 to get the other plane. So would that be conidental or parallel and distinct?

    • 2 years ago
  5. bahrom7893
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    that should be parallel and distinct.. if u can just multiply them by a scalar, but i suck at this, so idk.. @Mertsj @Zarkon

    • 2 years ago
  6. bahrom7893
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    @amistre64 @satellite73 @myininaya

    • 2 years ago
  7. bahrom7893
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    @LagrangeSon678

    • 2 years ago
  8. IsTim
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    Wait. Maybe I'll try something out here.

    • 2 years ago
  9. Zarkon
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    how is [2,3,7] the normal vector?

    • 2 years ago
  10. IsTim
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    Er, I just looked at my notes and inferred that...

    • 2 years ago
  11. Zarkon
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    if 2x+4y-7z-2=0 is your equation then <2,4,7> is the normal vector

    • 2 years ago
  12. Zarkon
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    <2,4,-7>

    • 2 years ago
  13. bahrom7893
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    Zarkon to the rescue!!!!

    • 2 years ago
  14. IsTim
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    Ok, got that. For the other then, it must be 4,6,-14?

    • 2 years ago
  15. Zarkon
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    yes

    • 2 years ago
  16. IsTim
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    So from this, how would I determine the answer? Or do I need more?

    • 2 years ago
  17. LagrangeSon678
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    if the planes are parrallel then the cross product of their normal vectors should be 0

    • 2 years ago
  18. Zarkon
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    two plane are parallel iff their normal vectors are parellel

    • 2 years ago
  19. IsTim
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    I'll try that cross product thing. Thanks guys. I'lll cry out if I have a problem.

    • 2 years ago
  20. Zarkon
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    two non zero vectors \(\vec{v}\) and \(\vec{u}\) are parallel iff \(\vec{v}=c\vec{u}\) for some scalar \(c\)

    • 2 years ago
  21. IsTim
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    Pardon?

    • 2 years ago
  22. Zarkon
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    is one of the vectors a constant multiple of the other?

    • 2 years ago
  23. IsTim
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    The first one, multiplied by 2, equals the second one.

    • 2 years ago
  24. Zarkon
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    really?

    • 2 years ago
  25. IsTim
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    IT seemed so...

    • 2 years ago
  26. Zarkon
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    if you have the equations 2x+4y-7z-2=0 4x+6y-14z-8=0 then you have the normal vectors <2,4,-7> and <4,6,-14> are these constant multiples of each other?

    • 2 years ago
  27. IsTim
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    That 4y was suppose to be a 3y....

    • 2 years ago
  28. IsTim
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    I did mistype that. No wonder my confusion. And probably yours...

    • 2 years ago
  29. Zarkon
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    then <4,6,-14>=2<2,3,-7> and so they are parallel...and therefore their planes are parallel

    • 2 years ago
  30. IsTim
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    And distinct??

    • 2 years ago
  31. Zarkon
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    yes

    • 2 years ago
  32. IsTim
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    Awesome. Thank you. This was relatively simple after all...

    • 2 years ago
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