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IsTim

  • 4 years ago

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

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

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

  4. IsTim
    • 4 years ago
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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?

  5. bahrom7893
    • 4 years ago
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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

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

  7. bahrom7893
    • 4 years ago
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    @LagrangeSon678

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

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

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

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

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

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

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

  15. Zarkon
    • 4 years ago
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    yes

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

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

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

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

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

  21. IsTim
    • 4 years ago
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    Pardon?

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

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

  24. Zarkon
    • 4 years ago
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    really?

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

  26. Zarkon
    • 4 years ago
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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?

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

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

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

  30. IsTim
    • 4 years ago
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    And distinct??

  31. Zarkon
    • 4 years ago
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    yes

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

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