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A three dimensional Cartesian coordinate system, with origin O and axis lines X, Y and Z, oriented as shown by the arrows. The tick marks on the axes are one length unit apart. The black dot shows the point with coordinates x = 2, y = 3, and z = 4, or (2, 3, 4).
10 Νοε 2020 · Euclidean space has three mutually perpendicular coordinate axes (\(x, y\) and \(z\)), and three mutually perpendicular coordinate planes\index{plane!coordinate}: the \(xy\)-plane, \(yz\)-plane and \(xz\)-plane (Figure \(\PageIndex{2}\) ).
In three dimensions, we define coordinate planes by the coordinate axes, just as in two dimensions. There are three axes now, so there are three intersecting pairs of axes. Each pair of axes forms a coordinate plane: the xy x y -plane, the xz x z -plane, and the yz y z -plane (Figure 5).
These three planes intersect along the lines X′OX, Y′OY and Z′OZ, and are respectively called the x, y and z-axes. However, point O is called the origin of the coordinate system. The representation of coordinate axes in three dimensions is given below.
16 Νοε 2022 · So, in a 3-D coordinate system this is a plane that will be parallel to the \(yz\)-plane and pass through the \(x\)-axis at \(x = 3\). Here is the graph of \(x = 3\) in \(\mathbb{R}\).
Find the equation of the plane passing through \((1,2,3)\) and \((1,-3,2)\) and parallel to the \(z\)-axis.
21 Δεκ 2020 · The obvious way to make this association is to add one new axis, perpendicular to the \(x\) and \(y\) axes we already understand. We could, for example, add a third axis, the \(z\) axis, with the positive \(z\) axis coming straight out of the page, and the negative \(z\) axis going out the back of the page.
