space. For example, a vector in three-dimensional space can be decomposed with respect to two axes, respectively normal, and tangent to a surface (see figure). Moreover, the radial and tangential components of a vector relate to the radius of rotation of an object. The former is parallel to the radius and the latter is orthogonal to it. In these cases, each of the components may be in turn decomposed with respect to a fixed coordinate system or basis set (e.g., a global coordinate system, or inertial reference frame). Basic properties The following section uses the Cartesian coordinate system with basis vectors and assumes that all vectors have the origin as a common base point. A vector a will be written as Equality Two vectors are said to be equal if they have the same magnitude and direction. Equivalently they will be equal if their coordinates are equal. So two vectors and are equal if Opposite, parallel, and antiparallel vectors Two vectors are opposite if they have the same magnitude but opposite direction. So two vectors and are opposite if Two vectors are parallel if they have the same direction but not necessarily the same magnitude, or antiparallel if they have opposite direction but not necessarily the same magnitude. Addition and subtraction The sum of a and b of two vectors may be defined as The resulting vector is sometimes called the resultant vector of a and b. The addition may be represented graphically by placing the tail of the arrow b at the head of the arrow a, and then drawing an arrow from the tail of a to the head of b. The new arrow drawn represents the vector a + b, as illustrated below: This addition method is sometimes called the parallelogram rule because a and b form the sides of a parallelogram and a + b is one of the diagonals. If a and b are bound vectors that have the same base point, this point will also be the base point of a + b. One can check geometrically that a + b = b + a and (a + b) + c = a + (b + c). The difference of a and b is Subtraction of two vectors can be geometrically illustrated as follows: to subtract b from a, place the tails of a and b at the same point, and then draw an