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The standard orientation, where the xy-plane is horizontal and the z-axis points up (and the x- and the y-axis form a positively oriented two-dimensional coordinate system in the xy-plane if observed from above the xy-plane) is called right-handed or positive. 3D Cartesian coordinate handedness. The name derives from the right-hand rule.
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
For any point, the abscissa is the first value (x coordinate), and the ordinate is the second value (y coordinate). In mathematics, the abscissa (/ æ b ˈ s ɪ s. ə /; plural abscissae or abscissas) and the ordinate are respectively the first and second coordinate of a point in a Cartesian coordinate system: [1] [2]
In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away.
For example, in the plane, if Cartesian coordinates (x, y) and polar coordinates (r, θ) have the same origin, and the polar axis is the positive x axis, then the coordinate transformation from polar to Cartesian coordinates is given by x = r cosθ and y = r sinθ.
In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.
The axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z.The geometrical definition (sometimes referred to as static) begins by defining the line of nodes (N) as the intersection of the planes xy and XY (it can also be defined as the common perpendicular to the axes z and Z and then written as the vector product N = z × Z).
In mathematics, an orientation of a curve is the choice of one of the two possible directions for travelling on the curve. For example, for Cartesian coordinates, the x-axis is traditionally oriented toward the right, and the y-axis is upward oriented.