Point

A point in geometry is a specific location in space. It has no dimensions, only position. Points are fundamental entities in geometry and are used to define other geometrical shapes, such as lines and planes.

In a given coordinate system, a point is represented by coordinates. In a two-dimensional Cartesian coordinate system, a point is represented by an ordered pair of numbers , where is the distance along the -axis, and is the distance along the -axis. For example, the point is units along the x-axis and units along the -axis from the origin.

In three-dimensional space, a point is represented by an ordered triple of numbers , specifying its position along the , , and axes.

Points are essential in many areas of mathematics, including algebra, geometry, and calculus, as well as in physics, engineering, computer graphics, and more.

Vector

A vector is a mathematical object represented by an ordered list of numbers called components, which define its magnitude and direction in a multi-dimensional space.