Figure 1 Coordinate system

Figure 2.5

Figure 2.6

Figure 2.7a

Figure 2.7b

By using polygon method, more than two vectors can be added as shown in Figure 2.5. The resultant vector sum is the vector drawn from the tail of the first vector to the tip of the last vector, . The order in which you add vectors is unimportant. But the directions and the magnitudes of the vectors should not be changed.
It is sometimes necessary to subtract one vector from another. To subtract B from A, for instance, we first form the negative of B denoted – B, a vector that has the same length as В but points in the opposite directions as shown in Figure 2.6. When we add -B to A, resultant vector R = A – B
Example 1: Find resultant vector of Figure 2.7a
Solution: We will use polygon method. Resultant vector is found as shown in Figure 2.7b


Multiplying or Dividing a Vector by a Scalar
Multiplying or dividing a vector by a scalar gives a vector. For example, if vector is multiplied by the scalar number 3, the result, written 3 , is a vector with a magnitude three times that of and pointing in the same direction. If we multiply vector by the scalar - 3, the result is - 3 , a vector with a magnitude three times that of and pointing in the opposite direction (because of the negative sign).