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chrisplusian

  • one year ago

Linear algebra help dealing with the equation of a plane....please see attachment

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  1. chrisplusian
    • one year ago
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  2. chrisplusian
    • one year ago
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    I need help with 1.12, I have tried the problem twice and no luck proving it

  3. dan815
    • one year ago
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    which part do u need help with the cartesian equation or the proof

  4. anonymous
    • one year ago
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    the first part of the question is simple getting you familiar with transforming a set of parametric equations into a cartesian equation

  5. anonymous
    • one year ago
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    perhaps reading your notes on this will jog your memory

  6. chrisplusian
    • one year ago
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    Bout to upload what I did give me just a second

  7. chrisplusian
    • one year ago
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    @dan815 I Know if I can get both of these planes into Cartesian equations I can show that the normal vector is a scalar multiple of the other and that will prove the planes are parallel. Then showing any point on both planes is the same will prove they are the same plane. The problem is I can't get the Cartesian equations in a way that shows the normal vectors are the same. If the normal vectors are not the same then they can't be the same plane

  8. chrisplusian
    • one year ago
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    @chris00 thanks for the tip about reading my notes, that never occurred to me

  9. chrisplusian
    • one year ago
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  10. dan815
    • one year ago
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    ah okay thats quite a bit of work

  11. chrisplusian
    • one year ago
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    Is there an easier way?

  12. dan815
    • one year ago
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    the point 1,1,1 should satisfy both equations correct?

  13. chrisplusian
    • one year ago
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    Well yes, but it doesn't prove they are the same plane

  14. dan815
    • one year ago
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    we will use that fact to prove it

  15. chrisplusian
    • one year ago
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    Ok

  16. dan815
    • one year ago
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    all we need are 2 things to be satisfied, both of them should have the same normal direction, and one point that is common,

  17. chrisplusian
    • one year ago
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    agreed

  18. dan815
    • one year ago
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    from the 2 equations you derived, i can say there has been a mistake as both of the normal lines are not equal

  19. chrisplusian
    • one year ago
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    That is what I thought but i can't see where. I actually did it twice and got the same exact thing so I figured there must be a mistake in the logic I used to derive the equations rather than a mistake in arithmetic or algebra

  20. dan815
    • one year ago
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    http://prntscr.com/8m15ta

  21. chrisplusian
    • one year ago
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    Because I came up with the same two equations both times

  22. dan815
    • one year ago
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    okay can u compute that, and show mw the 2 normal vectors you get again

  23. chrisplusian
    • one year ago
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    The way you annotated it?

  24. chrisplusian
    • one year ago
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    I get what your saying, and it makes perfect sense, but this professor wants us to show the Cartesian equations and then use the normal vectors in those equations to show they are parallel normal vectors.

  25. chrisplusian
    • one year ago
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    And this problem follows along those lines, because the first step is to find the Cartesian equation of the first line.

  26. dan815
    • one year ago
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    yep u can get the cartesian equations this way too

  27. dan815
    • one year ago
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    suppose you have a normal vector <a,b,c> then your plane equations is ax+by+cz=d now you can solve for d, by plugging in one of your known points for example the (1,1,1)

  28. dan815
    • one year ago
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    you repeat the same process for equation 2

  29. chrisplusian
    • one year ago
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    Ah, I see where your going and I didn't think of it that way. Let me try that way and see if I come up with an answer. Thank you

  30. dan815
    • one year ago
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    then you will see that a point in equation 1 exists in equation 2 as well, then these 2 places must coincide, because any 2 planes with the same normal vector direction will be parralel and can* only have a similiar point if they are in fact coincident

  31. anonymous
    • one year ago
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    so you can check your answers, the first parametric eq has carteisian form: \[3x _{1}-4x _{2}+2_{3}=1\] second one has cartesian form: \[-24x _{1}+32x _{2}-16x _{3}=-8\] now if u divide the second equation by -8 on both sides, you will see it is simply the cartesian equation of the first plane

  32. anonymous
    • one year ago
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    but as @dan815 said, its important to find the normal vector in these questions

  33. anonymous
    • one year ago
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    |dw:1443579442336:dw|

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