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3.1. Definition of a rectangular Cartesian coordinate system

Lecture



A rectangular Cartesian coordinate system (PDK) consists of a fixed point O (the center of the coordinate system ) and three intersecting in it, mutually perpendicular direction lines O x , O y , O z ( axes of the coordinate system ). Directions are chosen so that the straight lines form the right three vectors.

  3.1.  Definition of a rectangular Cartesian coordinate system

Fig. 2

The unit vectors defining the directions of the axes O x , O y , O z are denoted by the letters i, j, k and form an orthonormal basis (Fig. 2).

Vector   3.1.  Definition of a rectangular Cartesian coordinate system called the radius vector of a point   3.1.  Definition of a rectangular Cartesian coordinate system . Vector coordinates   3.1.  Definition of a rectangular Cartesian coordinate system relative to the base i, j, k are coordinates of the point   3.1.  Definition of a rectangular Cartesian coordinate system i.e. if a   3.1.  Definition of a rectangular Cartesian coordinate system (   3.1.  Definition of a rectangular Cartesian coordinate system ), then   3.1.  Definition of a rectangular Cartesian coordinate system - point with coordinates p x , p y , p z .

Because   3.1.  Definition of a rectangular Cartesian coordinate system then   3.1.  Definition of a rectangular Cartesian coordinate system .

  3.1.  Definition of a rectangular Cartesian coordinate system

Fig. 3

If vectors are viewed on a plane, then the PDK consists of two perpendicular axes O x , O y with the guide orta i, j ( i = {1; 0}, j = {0; 1}) (Fig. 3).


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Linear Algebra and Analytical Geometry

Terms: Linear Algebra and Analytical Geometry