1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solve the following system and interpret the result geometrically

  1. Sep 2, 2008 #1
    Solve the following system and interpret the result geometrically

    3x + 4y + 5z - 18 = 0
    2x - y + 8z - 13 = 0
    -x + 17y + 25z + 11 = 0


    My answer:
    3x + 4y + 5z – 18 = 0 (1)
    2x – y + 8z – 13 = 0 (2)
    -x + 17y + 25z + 11 = 0 (3)

    Multiply (1) by 2 and (2) by 3

    6x + 8y + 10z – 36 = 0
    6x – 3y + 24z – 39 = 0

    Subtract the two equations

    11y – 14z + 3 = 0 (4)

    Multiply equation (3) by -3

    3x – 51y – 75z – 33 = 0

    Subtract the equation from (1)

    55y + 80z + 15 = 0

    Simplify

    11y + 16z + 3 = 0 (5)

    We now have the new system
    11y – 14z + 3 = 0 (4)
    11y + 16z + 3 = 0 (5)

    Subtract (4) from (5)

    30z = 0


    this is as far as i got...i'm not sure if it is correct and if it is correct i dont know what it geometrically represents.
    any guidance is appreciated
    Thanks in advance
     
  2. jcsd
  3. Sep 2, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You're doing fine so far. Now finish by finding x and y. If you think of x,y,z as three dimensional coordinates then the graph of each of those equations is very simple geometrical figure. Can you name it? Solving them simultaneously is the same as finding the intersection in geometric language.
     
  4. Sep 3, 2008 #3
    Solve for z
    z = 0

    substitute z = 0 into equation (4)

    11y – 14(0) + 3 = 0

    11y + 3 = 0
    y = 3/11

    substitute y and z into equation (1) to find x

    3x + 4(3/11) + 5(0) – 18 = 0
    x = 5.6

    Therefore the planes intersect at the point (5.6, 0.273, 0) and are parallel to the z axis.

    am i getting somewhere?
    THANKS
     
  5. Sep 3, 2008 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are getting somewhere, but you are being pretty sloppy on the way. Shouldn't y=(-3/11)? Once you have (x,-3/11,0) then, sure, you have three planes that intersect in that point. But why would say any of them is parallel to the z axis? What would the equation of a plane parallel to the z axis look like?
     
  6. Sep 3, 2008 #5
    i got confused for some reason i thought because the z value of the point was zero there was a plane parallel to the z-axis...
    so in the end would i simply say:
    substitute y and z into equation (1) to find x

    3x + 4(-3/11) + 5(0) – 18 = 0
    x = -6.4

    Therefore the three planes intersect at the point (-6.4, 0.273, 0)
     
  7. Sep 3, 2008 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Now you've got the x value wrong. :( Why don't you just express them all as fraction like -3/11. That way you don't have to worry about round off.
     
  8. Sep 3, 2008 #7
    3x + 4(-3/11) + 5(0) – 18 = 0
    x = -70/11

    Therefore the three planes intersect at the point (-70/11, -3/11, 0)
     
  9. Sep 3, 2008 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are making the same mistake as with y. The SIGN is wrong. Figure out what you are doing wrong that is causing this to happen and don't do it again!
     
  10. Sep 3, 2008 #9
    ahhh...i wasn't switching the sign when I added it to the R.S so the point is (70/11, -3/11, 0)
     
  11. Sep 3, 2008 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Riggght.
     
  12. Sep 3, 2008 #11
    YAY! Thanks for the help!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Solve the following system and interpret the result geometrically
Loading...