# Homework Help: 3 dimension coordinate systems

1. Sep 15, 2007

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. Sep 15, 2007

### D H

Staff Emeritus
Can you describe the solution to x=0? To xy=0? Start simple, work your way up.

3. Sep 15, 2007

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?

4. Sep 15, 2007

### D H

Staff Emeritus
Describe y=constant (or x=constant) in simple terms. Zero is just a special constant.

5. Sep 15, 2007

so z x and y and all constants....and at least one must be 0? thats how i would describe it?

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 ! :)

6. Sep 15, 2007

### D H

Staff Emeritus
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.

7. Sep 15, 2007

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
8. Sep 15, 2007

### D H

Staff Emeritus
Not so fast, grasshopper. What simple geometric shape does y=mx+b represent in R2?

9. Sep 15, 2007

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?

10. Sep 15, 2007

### D H

Staff Emeritus
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?

11. Sep 15, 2007

parabola?

and the special name being the axis?

12. Sep 15, 2007

### D H

Staff Emeritus
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.

13. Sep 15, 2007

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

14. Sep 15, 2007

ooo maybe at something???? would xyz=0 refer to any point on an axis?

15. Sep 16, 2007

### HallsofIvy

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.

16. Sep 16, 2007

so then would it be any point on the plane xy, xz, yz ?

17. Sep 16, 2007

### D H

Staff Emeritus
Bingo.

18. Sep 16, 2007