Päättyävektori

Päättyävektori, often translated as terminal vector or endpoint vector, is a concept used in mathematics, particularly in geometry and vector algebra. It refers to the vector that originates from a reference point, typically the origin, and ends at a specific point in space. The terminal vector essentially defines the position of that point relative to the origin.

In a coordinate system, a point P with coordinates (x, y) in two dimensions or (x, y, z) in three dimensions can be represented by its terminal vector. If the origin is denoted by O, the terminal vector is the vector OP. The components of the terminal vector are identical to the coordinates of the point it represents. For example, the terminal vector for point P(3, 4) in 2D is the vector <3, 4>.

Terminal vectors are fundamental for describing displacement, position, and transformations in vector spaces. They are distinguished from displacement vectors, which represent the change in position between two arbitrary points, whereas a terminal vector always has a fixed starting point (the origin). Understanding terminal vectors is crucial for operations like vector addition, subtraction, and scalar multiplication, as these operations are performed on the components of the vectors, which are directly derived from the point's coordinates.