® If we have two vectors , given in component form as and λ any scalar, then b i b k ; λ = a i a k λ + λ + λ ; ; c c Historical Note The word vector has been derived from a Latin word vectus , which means “to carry”. The germinal ideas of modern vector theory date from around when Caspar Wessel ( - ) and Jean Robert Argand ( - ) described that how a complex number a + ib could be given a geometric interpretation with the help of a directed line segment in a coordinate plane. William Rowen Hamilton ( - ) an Irish mathematician was the first to use the term vector for a directed line segment in his book Lectures on Quaternions ( ). Hamilton’s method of quaternions (an ordered set of four real numbers given as: ˆ ˆ , , , bi cj dk i j k following certain algebraic rules) was a solution to the problem of multiplying vectors in three dimensional space.
Though, we must mention here that in practice, the idea of vector concept and their addition was known much earlier ever since the time of Aristotle ( - B.C.), a Greek philosopher, and pupil of Plato ( - B.C.). That time it was supposed to be known that the combined action of two or more forces could be seen by adding them according to parallelogram law. The correct law for the composition of forces, that forces add vectorially, had been discovered in the case of perpendicular forces by Stevin-Simon ( - ). In A.D., he analysed the principle of geometric addition of forces in his treatise DeBeghinselen der Weeghconst (“Principles of the Art of Weighing”), which caused a major breakthrough in the development of mechanics.
But it took another years for the general concept of vectors to form. In the , Josaih Willard Gibbs ( - ), an American physicist and mathematician, and Oliver Heaviside ( - ), an English engineer, created what we now know as vector analysis , essentially by separating the real ( scalar ) part of quaternion from its imaginary ( vector ) part. In and , Gibbs printed a treatise entitled Element of Vector Analysis . This book gave a systematic and concise account of vectors.
However, much of the credit for demonstrating the applications of vectors is due to the D. Heaviside and P.G. Tait ( - ) who contributed significantly to this subject.