vektorösszeg

Vektorösszeg refers to the operation of adding two or more vectors together. Vectors are mathematical objects that possess both magnitude and direction. When vectors are added, the resulting vector, known as the resultant vector or simply the sum, represents the combined effect of the individual vectors.

There are several ways to visualize and compute vector sums. The parallelogram law states that if two vectors are represented as adjacent sides of a parallelogram, their sum is represented by the diagonal originating from the common vertex. Another common method is the head-to-tail rule, where the tail of one vector is placed at the head of another. The resultant vector then connects the tail of the first vector to the head of the last vector.

Mathematically, vector addition is performed by adding the corresponding components of the vectors. For example, if vector A = (Ax, Ay) and vector B = (Bx, By), their sum, vector C = A + B, is calculated as C = (Ax + Bx, Ay + By). This component-wise addition applies to vectors in any number of dimensions.

The concept of vector summation is fundamental in physics and engineering, used to determine quantities such as net force, velocity, and displacement. It is also crucial in various fields of mathematics, including linear algebra and geometry. The order of addition does not affect the resultant vector; vector addition is commutative (A + B = B + A) and associative (A + (B + C) = (A + B) + C).