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The line segments AB and CD are perpendicular to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Although many authors use the two terms perpendicular and orthogonal interchangeably, the term perpendicular is more specifically used for lines and planes that intersect to form a right angle, whereas orthogonal is used in generalizations ...
In Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90° (radians), or one of the vectors is zero. [4] Hence orthogonality of vectors is an extension of the concept of perpendicular vectors to spaces of any dimension.
In geometry, two circles are said to be orthogonal if their respective tangent lines at the points of intersection are perpendicular (meet at a right angle). A straight line through a circle's center is orthogonal to it, and if straight lines are also considered as a kind of generalized circles , for instance in inversive geometry , then an ...
The conic sections – circles, ellipses, parabolas, and hyperbolas – are plane sections of a cone with the cutting planes at various different angles, as seen in the diagram at left. Any cross-section passing through the center of an ellipsoid forms an elliptic region, while the corresponding plane sections are ellipses on its surface.
In machining, the rake angle is a parameter used in various cutting processes, describing the angle of the cutting face relative to the workpiece. There are three types of rake angles: positive, zero or neutral, and negative. Positive rake: A tool has a positive rake when the face of the cutting tool slopes away from the cutting edge at inner side.
When = =, the projection is said to be "orthographic" or "orthogonal". Otherwise, it is "oblique". Otherwise, it is "oblique". The constants a {\displaystyle a} and b {\displaystyle b} are not necessarily less than 1, and as a consequence lengths measured on an oblique projection may be either larger or shorter than they were in space.
A conformal map acting on a rectangular grid. Note that the orthogonality of the curved grid is retained. While vector operations and physical laws are normally easiest to derive in Cartesian coordinates, non-Cartesian orthogonal coordinates are often used instead for the solution of various problems, especially boundary value problems, such as those arising in field theories of quantum ...
In the diagram, the circle contained in the front face is undistorted. If the image of a circle is an ellipse, one can map four points on orthogonal diameters and the surrounding square of tangents and in the image parallelogram fill-in an ellipse by hand.