![]() ![]() There is a one-to-one correspondence between the points in space and the ordered triples in R 3. The Cartesian product RxRxR is the set of all ordered triples of real numbers and is denoted by R 3. The Cartesian product RxR is the set of all ordered pairs of real numbers and is denoted by R 2. Z is the directed distance from the xy-plane to the point P.Įxample - Distance of Point from the Coordinate Planesįor the point P(3, 2, 6), determine the directed distance from each coordinate plane. Y is the directed distance from the xz-plane to the point P, and X is the directed distance from the yz-plane to the point P, Point Coordinates as Distances from Coordinate Planes The xz-plane is the plane that contains the x- and z-axes. The yz-plane is the plane that contains the y- and z-axes ![]() The xy-plane is the plane that contains the x- and y-axes The three coordinate axes determine the three coordinate planes. To locate a point P( a, b, c), we can start at the origin O, move a units along the x-axis, then b units parallel to the y-axis, and then c units parallel to the z-axis. Hence, space is called three-dimensional. In space, we use three coordinate axes, the x-axis, y-axis and z-axis, (each of which is perpendicular to the other two) that meet at a point O, the origin.Ī point in space can be represented as an ordered triple (a, b, c) of real numbers, where a is the x-coordinate, b is the y-coordinate and c is the z-coordinate. Hence, a plane is called two-dimensional. In a plane, we use two coordinate axes, the x-axis and y-axis, that are perpendicular to each other to determine the location of any point in the plane.Ī point in the plane can be represented as an ordered pair ( a, b) of real numbers, where a is the x-coordinate and b is the y-coordinate. ![]() 13.1 Three-Dimensional Coordinate Systems ![]()
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