This article is about the vectors mainly used in physics and engineering to represent directed quantities. It was first used by 18th century astronomers investigating planet rotation vectors and tensors in engineering and physics pdf the Sun.

Many other physical quantities can be usefully thought of as vectors. The concept of vector, as we know it today, evolved gradually over a period of more than 200 years. About a dozen people made significant contributions. Working in a Euclidean plane, he made equipollent any pair of line segments of the same length and orientation. The algebraically imaginary part, being geometrically constructed by a straight line, or radius vector, which has, in general, for each determined quaternion, a determined length and determined direction in space, may be called the vector part, or simply the vector of the quaternion.

Grassmann’s work was largely neglected until the 1870s. This approach made vector calculations available to engineers and others working in three dimensions and skeptical of the fourth. 1881, presents what is essentially the modern system of vector analysis. Gibb’s lectures, which banished any mention of quaternions in the development of vector calculus. In this context, vectors are abstract entities which may or may not be characterized by a magnitude and a direction.

This article is about vectors strictly defined as arrows in Euclidean space. In either case, the magnitude of the vector is 15 N. 4 m, depending on its direction, and its magnitude would be 4 m regardless. Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has magnitude, has direction, and which adheres to the rules of vector addition. Examples of quantities that have magnitude and direction but fail to follow the rules of vector addition: Angular displacement and electric current. Consequently, these are not vectors.