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- The planes XOY, YOZ and ZOX, are called the XY-plane, YZ-plane, and the ZX-plane, respectively; these are also known as the three coordinate planes.
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What are Xoy yoz & Zox coordinate planes?
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The coordinate surfaces of the Cartesian coordinates (x, y, z). The z-axis is vertical and the x-axis is highlighted in green. Thus, the red plane shows the points with x = 1, the blue plane shows the points with z = 1, and the yellow plane shows the points with y = −1.
Aug 17, 2024 · Each pair of axes forms a coordinate plane: the \(xy\)-plane, the \(xz\)-plane, and the \(yz\)-plane (Figure \(\PageIndex{4}\)). We define the \(xy\)-plane formally as the following set: \(\{(x,y,0):x,y∈ℝ\}.\) Similarly, the \(xz\)-plane and the \(yz\)-plane are defined as \(\{(x,0,z):x,z∈ℝ\}\) and \(\{(0,y,z):y,z∈ℝ\},\) respectively.
A plane in 3D coordinate space is determined by a point and a vector that is perpendicular to the plane. Let P_ {0}= (x_ {0}, y_ {0}, z_ {0} ) P 0 = (x0,y0,z0) be the point given, and \overrightarrow {n} n the orthogonal vector.
We define the xy-plane formally as the following set: {(x, y, 0): x, y ∈ ℝ}. {(x, y, 0): x, y ∈ ℝ}. Similarly, the xz -plane and the yz -plane are defined as { ( x , 0 , z ) : x , z ∈ ℝ } { ( x , 0 , z ) : x , z ∈ ℝ } and { ( 0 , y , z ) : y , z ∈ ℝ } , { ( 0 , y , z ) : y , z ∈ ℝ } , respectively.
Locate points in space using coordinates. As we have learned, the two-dimensional rectangular coordinate system contains two perpendicular axes: the horizontal [latex]x [/latex]-axis and the vertical [latex]y [/latex]-axis.
What is the three-dimensional coordinate system? The three-dimensional coordinate system contains an origin (normally denoted by O) and formed by three mutually perpendicular coordinate axes: the x -axis, y -axis, and the z -axis.
