# Motion in 2d or 3d

In physics, a vector is a quantity that has magnitude and direction. A vector can be understood as an arrow in space, whose magnitude is its length and whose direction points in the direction of its length. The magnitude of a vector is defined as its length, and the direction of a vector is the direction that its length points in space. If a vector has zero magnitude, it is said to be perpendicular to itself. A more elaborate example of a vector is where a particular vector has components along the three axes of a Cartesian coordinate system. The components are usually called "x", "y", and "z". This is called a "vector quantity". If it is a vector in the direction of the x-axis, for example, then it is usually called "x", if it is a vector along the y-axis, it is usually called "y", and if it is along the z-axis, it is usually called "z". In three dimensions, a vector quantity has components for the three axes of the three dimensional Cartesian coordinate system. In SI units, a vector quantity has an "m" component along each of the three axes, for a total of six components, and "N" components perpendicular to each of the three axes (i.e. perpendicular to the three Cartesian coordinate system axes). In Imperial units, the components are designated "x", "y" and "z". In mathematics, a vector quantity is an object that has both magnitude and direction. We would like to be able to define a vector quantity in such a way that we can add vectors and multiply them by scalars, just as we can add and multiply scalars. In particular, we can define a vector quantity as a function of a scalar and a direction. A vector quantity, in this sense, is a function. Just as a function of two variables may be defined by three equations, so a function of three variables may be defined by six equations. Often the two axes are called "x" and "y", and the third axis is called "z". Vectors that have magnitudes and directions (i.e., their components) are called "n"-vectors, while vectors that can be added to form a new vector are called "n"-tuple vectors. The concept of a vector is of fundamental importance in physics, as well as in many other branches of mathematics, engineering and the physical sciences. Vectors form the basis of vector calculus, which is the mathematical foundation for much of applied mathematics, physics, and engineering. Many geometric and physical properties are scalar properties, but when they are described at an appropriate level of detail, become vector quantities.