Which axis is which in 3 Dimensional system?

Question

i'm a little confused.

1)Which axis is which in 3 Dimensional system?

2)Does it matter if I switch the x-axis to y-axis?

Answer 1

1) Traditionally, the Cartesian coordinate system in $\mathbb{R}^3$ uses the notation $(x,y,z)$ to denote a general point in three-space. The reason is that these letters appear in this order in the alphabet. Now the $x$ axis is obtained by putting zeros for the $z$ and $y$, so that you are left with points of the form $(x,0,0)$. Thus, $(1,0,0), (-2,0,0)$ are points on the $x$-axis. Similarly, the $y$ and the $z$-axis are obtained by putting zeros for the other two, respectively.

2) Once you fix a coordinate system, you have to be careful when you switch axes. This is because representation of points and functions on them usually depends on the choice of a particular coordinate system. What is, after all, the meaning of the point $(1,0,0)$? If you assume the natural coordinate system (the one described in 1)), this is a point lying one unit of distance to the perfect east of the origin $(0,0,0)$. Note that this latter description, (one unit of distance to the east), used the notion of distance and direction (namely, "east"). If you were to switch the axes now, and decide that points to the east (and west) of the origin are the $y$-axis, then the same point would have to be written as $(0,1,0)$.

Answer 2

The way I understand it is:
$(0\mid 0\mid 0)$ is said to be "the origin."

[b is any non-zero number] $(b\mid 0\mid 0),(0\mid b\mid 0),(0\mid 0\mid b)$ are said to be on the x-axis, the y-axis and the z-axis, respectively.

[b and c are any non-zero numbers]
$(0\mid b\mid c),(b\mid 0\mid c),(b\mid c\mid 0)$ are said to be on the yz-plane, the xz-plane and the xy-plane, respectively.

[b, c and d are any non-zero numbers] $(b\mid c\mid d)$ is said not to be in any of the above categories.

The x-, y- and z-coördinates are referred to by the terms "abscissa," "ordinate" and "applicate," respectively.

There are two orientations of the three axes, called "right-hand" and "left-hand," where one would associate a positive axis with the thumb, index finger and insult finger as a mnemonic.

Good hunting!