2018年4月17日 · This is a 2-dimensional flat plane and locations on the plane can be identified by an (x,y) Coordinate. Z-Coordinates are found in a geometric setting called three-dimensional space. Unlike the 2d flat xy plane, to identify a location in 3d space, three parameters (variables/values) are required to determine a position/location (x,y,z)

2019年9月23日 · This reference is used in the Machine Tool Trades. It is taught that the Z axis is referencing the vertical axis which is the center of rotation referred to as the axial plane. Figure 3 This denotes the rotational axis of a CNC machine. This does not however denote a moniker of X, Y or Z. The direction of the thumb is referencing axial plane.

2014年9月26日 · A standard x,y graph is like a 2D square. The length of the square is the x-axis and the height of the square is the y-axis, and you can use these to plot two variables against each other (eg, foot size and leg length). However, if you want to plot three variables against each other (eg, foot size, leg length and waist size) then you can make a 3D graph that looks like a …

The z-axis, is also sometimes known as.... the z-axis. If you are drawing the axes as they are typically taught in school, the z-axis becomes the "height", the y-axis is "width" and I guess you could say that the x-axis becomes "depth" or "length"

2017年4月13日 · For 3D diagrams, the names "abscissa" and "ordinate" are rarely used for x and y, respectively. When they are, the z-coordinate is sometimes called the applicate. The words abscissa, ordinate and applicate are sometimes used to refer to coordinate axes rather than the coordinate values.

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2021年10月6日 · An axis is nothing more than the extension of a unit vector in a specific direction. In your case, you are using rectangular coordinates, so the unit vectors are referred to some "privileged" directions:

$\begingroup$ Both ways obey the right hand rule in that a vector in the positive x axis cross the vector in the positive y axis produces a vector in the positive z axis. In fact, the first way I graphed it, the force is "out of the page" which seems like it's even more consistent, although I cannot concretely explain why it seems better to me ...

2021年6月14日 · For the Z axis rotation, you want to rotate through an angle whose tangent is $\frac{x}{y}$, so the rotation matrix is $$ \langle x,y,z\rangle \cdot \begin{pmatrix} \frac{y}{\sqrt{x^2+y^2}}& \frac{x}{\sqrt{x^2+y^2}}& 0 \\ -\frac{x}{\sqrt{x^2+y^2}} & \frac{y}{\sqrt{x^2+y^2}} & 0 \\ 0 & 0 & 1 \end{pmatrix} = \langle 0, \sqrt{x^2+y^2}, z\rangle.$$ …

There are two equivalent ways of doing this. Let $\hat x, \hat y, \hat z$ be your basis vectors. the first approach is to construct a rotation map that maps $\hat z \mapsto \hat z' = \hat n$.