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3 dimension coordinate systems

  1. Sep 15, 2007 #1
    1. The problem statement, all variables and given/known data

    Describe in words the region of R3 (3 dimension) represented by the following inequality.

    1)xyz=0

    2. Relevant equations

    none i know of

    3. The attempt at a solution


    no idea where to start. I know that this means one variable must be equal to 0, but i don't know how to classify it.

    for example

    x^2+y^2=r^2 is for a circle....

    x^2+y^2+z^2=r^2 is a sphere

    x^2 is a parabola

    y=mx+b is a line
    how would i clasify xyz... :)


    NUMBER 2!

    Write an inequality to describe the region.

    a) region consisting of the firts octant bounded by z=1 y=2 z=3


    what ive tried

    i'm nt sure if this means x is bounded by x=0 and x=1...or if it means x<=1 and can continue infinatly (same with y and z)

    and also, i think id have to make is such 6x=6 3y=6 2z=6 and make it in the form of x^2+y^2+z^2 >= 6 (or <=6 depending on the bounds)

    thanks for some input ! :)
     
  2. jcsd
  3. Sep 15, 2007 #2

    D H

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    Can you describe the solution to x=0? To xy=0? Start simple, work your way up.
     
  4. Sep 15, 2007 #3
    x=0 means there is only a y coordinate...so (0,y) and xy=0 means (0,y,z) or (x,0,z) or (0,0,z) so xyz=0 means that (x,y,0) or (x,0,z) or(0,y,z) or (x,0,0) or (0,y,0) or (0,0,z) or (0,0,0)

    but how do i relate this to some sort of shape? or would i just use what i did?
     
  5. Sep 15, 2007 #4

    D H

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    Describe y=constant (or x=constant) in simple terms. Zero is just a special constant.
     
  6. Sep 15, 2007 #5
    so z x and y and all constants....and at least one must be 0? thats how i would describe it?

    and how about the 2nd question i had?


    NUMBER 2!

    Write an inequality to describe the region.

    a) region consisting of the firts octant bounded by z=1 y=2 z=3


    what ive tried

    i'm nt sure if this means x is bounded by x=0 and x=1...or if it means x<=1 and can continue infinatly (same with y and z)

    and also, i think id have to make is such 6x=6 3y=6 2z=6 and make it in the form of x^2+y^2+z^2 >= 6 (or <=6 depending on the bounds)

    thanks for some input ! :)
     
  7. Sep 15, 2007 #6

    D H

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    Slow down, roadrunner. You are going too fast and in the wrong direction. You appeared to be having troubles with some very basic concepts, so I started simple. Lets start even simpler, with the equation x=c: What simple geometric shape does x=c represent in R1, R2, and R3? I'll give you a start: In R1 x=c represents a point.

    Now specialize to the special constant zero. In R3, the three geometric shapes defined by three equations x=0, y=0, and z=0 have special names.

    Finally, what does xyz=0 mean?

    Problem 2. What simple expression defines the first octant (use the standard definition here)? This is a simple relation on (x,y,z). Now all you have to do is shift this so that the reference point is not the origin.
     
  8. Sep 15, 2007 #7
    in R2 x=c means just a point also, and in R3?

    quesiton two

    X>=1 Y>=0 Z>=0 defins the firts octant. so would it be (x-1) +(y-2) + (y-3) >=0? that seems wrong, because that sitll doesnt show that x y and z have individual restrictions.

    edit!

    just noticed book said inequalities so can i just go x>=1 y>=2 z>=3
     
    Last edited: Sep 15, 2007
  9. Sep 15, 2007 #8

    D H

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    Not so fast, grasshopper. What simple geometric shape does y=mx+b represent in R2?
     
  10. Sep 15, 2007 #9
    a line
    but i thought you said just x=c?
    did you mean in R2 use y=mx+b and in R3 use another formula that relates x z y?
     
  11. Sep 15, 2007 #10

    D H

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    Start with y=mx+b. Its a line in R2. Now set m to zero and change that 'b' to c. You get y=0*x+c, or simply y=c. This is still a line. Now change the 'c' to zero. By the way, this line (y=0) has a special name. x=my+b is also an equation of a line. Now set m to zero and b to zero. This (x=0) is still a line, and this line has a special name also.

    To recap, in R1, the equation x=c represents a point, and in R2 it represents a line. What does this equation represent in R3?
     
  12. Sep 15, 2007 #11
    parabola?

    and the special name being the axis?
     
  13. Sep 15, 2007 #12

    D H

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    Stop guessing. How could it possibly be a parabola? A parabola "lives" in a plane, not in three dimensions. What is the next step in the progression a point, a line, a ... ?

    Someone else needs to help roadrunner here, I am off 'til tomorrow morning.
     
  14. Sep 15, 2007 #13
    circle?
    i said parabola cause c=point x=line so i assume enxt was x^2 which is a parabola....but it would be a circle
     
  15. Sep 15, 2007 #14
    ooo maybe at something???? would xyz=0 refer to any point on an axis?
     
  16. Sep 16, 2007 #15

    HallsofIvy

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    A very "relevant equation" is that if ab= 0 then either a= 0 or b= 0. If xyz= 0, then at least one of x, y, or z is 0. No, it is not "any point on an axis" because points on axes have two coordinates 0.
     
  17. Sep 16, 2007 #16
    so then would it be any point on the plane xy, xz, yz ?
     
  18. Sep 16, 2007 #17

    D H

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    Bingo.
     
  19. Sep 16, 2007 #18
    thanks man! haha
     
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