In vector analysis, the combined effect of two or more vectors is represented by a single vector called their combined vector. Visually, if the vectors are drawn head-to-tail, this combined vector connects the tail of the first vector to the head of the last. Mathematically, it is calculated by adding the corresponding components of the individual vectors. For example, if two vectors are represented by (3, 4) and (1, -2), their combined vector is (3+1, 4+(-2)) = (4, 2).
Determining this combined vector is fundamental in various fields. Physics uses it extensively to understand the net force acting on an object or the overall displacement of a moving body influenced by multiple forces or displacements. Engineering relies on this concept for structural analysis, designing bridges and buildings to withstand combined loads. Navigation employs vector addition for calculating the optimal course considering wind and currents. The historical development of this concept can be traced back to the work of mathematicians and physicists like Isaac Newton and Galileo Galilei, who laid the groundwork for modern vector analysis.
