Figure 1 Coordinate system

Figure 2.3b

Figure 2.3c

Figure 2.4

Ordinary arithmetic is used to add two or more scalar quantities of the same kind together. The same kind of arithmetic is used for vector quantities of the same kind, when the directions are the same as shown in Figure 2.2. What will we do, if the vectors are in different directions? To find resultant vector we will use different ways. We can add and subtract vectors by geo­metrically and mathematically. We geometrically add vectors in three different methods: triangle, parallelogram and polygon.
We are given two vectors as shown in Figure 2.3a. By using triangle method, we add the vectors as shown in Figure 2.3b. We can add two vectors by placing them head to tail. The vector A must be drawn such that, its direction is specified relative to a co­ordinate system. Then, draw vector В using this same scale and with the tail of B starting from the tip of A. Vector В must be drawn along the direction which makes the proper angle relative to vector A. The resultant vector, as shown Figure 2.3c, is the vector drawn from the tail of A to the tip of В.
The parallelogram rule of addition is shown in Figure 2.4 In this con­struction, the tails of the two vectors A and В are together and the resultant vector R is the diagonal of the parallelogram formed with A and B as its side.