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ranyai12

Please Help! Parameterize the plane that contains the three points (3,−5,−2), (10,−12,−10), and (25,0,5). r(s,t)=

  • 9 months ago
  • 9 months ago

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  1. ranyai12
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    I first assigned the points to P Q and R and then found PQ and PR and then put P+u<PQ>+v<PR> and I got <3+7s+22t,-5-7s+5t,-2-8s+7s> but got it wrong!

    • 9 months ago
  2. jim_thompson5910
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    what did you get for vector PQ

    • 9 months ago
  3. jim_thompson5910
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    btw, this page may help you out http://math.harvard.edu/~ytzeng/worksheet/0926_sol.pdf see page 3

    • 9 months ago
  4. ranyai12
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    I got <7,-7,-8>

    • 9 months ago
  5. ranyai12
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    Yes i looked at that and Im stll not sure what i dd wrong

    • 9 months ago
  6. jim_thompson5910
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    how about PR?

    • 9 months ago
  7. ranyai12
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    22,5,7

    • 9 months ago
  8. jim_thompson5910
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    ok, so far, so good

    • 9 months ago
  9. jim_thompson5910
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    I'm assuming you tried <3+7s+22t,-5-7s+5t,-2-8s+7t>and not <3+7s+22t,-5-7s+5t,-2-8s+7s> right?

    • 9 months ago
  10. ranyai12
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    i did it twice and got it wrong twice

    • 9 months ago
  11. jim_thompson5910
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    ok one sec

    • 9 months ago
  12. jim_thompson5910
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    does it specify at all which variables are the free variables (like x and y or x and z)?

    • 9 months ago
  13. ranyai12
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    no

    • 9 months ago
  14. jim_thompson5910
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    hmm well I managed to find a calculator that will give the equation of the plane

    • 9 months ago
  15. jim_thompson5910
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    that equation is -x-25y+21z-80 = 0 -x-25y+21z= 80 solve for x: -x-25y+21z= 80 -x = 80+25y-21z x = -80-25y+21z

    • 9 months ago
  16. jim_thompson5910
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    so if you let y = s and z = t, then you will get <x, y, z> = <-80-25y+21z, y, z> <x, y, z> = <-80-25s+21t, s, t>

    • 9 months ago
  17. jim_thompson5910
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    unfortunately there are many ways to parameterize the plane

    • 9 months ago
  18. ranyai12
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    can you please provide me with an example

    • 9 months ago
  19. jim_thompson5910
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    what do you mean

    • 9 months ago
  20. ranyai12
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    as in please show me a way o parameterize this

    • 9 months ago
  21. jim_thompson5910
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    well you could take the cross product of vectors PQ and PR

    • 9 months ago
  22. jim_thompson5910
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    that will give you the normal vector to the plane

    • 9 months ago
  23. ranyai12
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    what would i do then

    • 9 months ago
  24. jim_thompson5910
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    what do you get when you do the cross product

    • 9 months ago
  25. ranyai12
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    gimme a sec

    • 9 months ago
  26. ranyai12
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    -89i+113j+189k

    • 9 months ago
  27. jim_thompson5910
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    somewhat close, but that's not correct

    • 9 months ago
  28. ranyai12
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    what is it then?

    • 9 months ago
  29. jim_thompson5910
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    try it again

    • 9 months ago
  30. ranyai12
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    ok

    • 9 months ago
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