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qwerty11
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A friend asked me this question today. It kinda threw me for a loop. The cartesian coordinates system is a left handed coordinate system right, so therefroe they are defined by a left handed coordinate syste correct?
Not necessarily. That is an extremely common, but not universal, convention.Mark44 said:The Cartesian coordinate system is a right-handed system.
Or he/she is a geologist, or a radar technician, or a GPS specialist, or someone else who (danged annoyingly!) works with north-east-up coordinates.HallsofIvy said:Your friend is playing with your mind!
A left-handed coordinate system is a mathematical system used to represent points, lines, and shapes in three-dimensional space. It is based on the concept of three perpendicular axes, each representing a different dimension (x, y, and z). In a left-handed coordinate system, the x-axis points to the left, the y-axis points down, and the z-axis points away from the viewer.
In a left-handed coordinate system, unit vectors i, j, and k are used to represent the directions of the x, y, and z axes, respectively. These unit vectors have a magnitude of 1 and are used to define the direction and orientation of points, lines, and shapes in three-dimensional space.
In a left-handed coordinate system, unit vectors i, j, and k are perpendicular to each other. The i-axis is perpendicular to both the j-axis and k-axis, the j-axis is perpendicular to both the i-axis and k-axis, and the k-axis is perpendicular to both the i-axis and j-axis.
To represent a point in a left-handed coordinate system, you would use a combination of the three unit vectors. The coordinates of the point would be expressed as a linear combination of the unit vectors, with each vector representing a different direction. For example, the point (3, 2, 4) would be represented as 3i + 2j + 4k.
The use of a left-handed coordinate system is a convention that allows for consistency and standardization in mathematical calculations and visual representations in three-dimensional space. It is also important in fields such as physics and engineering, where the direction and orientation of objects and their movements are crucial for analysis and problem-solving.