Adding Vectors: Graphical Method

Another way to think about the previous problem is with vectors, which are little arrows whose orientation specifies direction and whose length specifies magnitude. The displacement along the river is represented as

FIGURE 1.1 Displacement along the river. with a length of 30 m, denoted as  and the displacement across the river,

denoted B,

FIGURE 1.2 Displacement across the river.

with length of 40 m. To re-construct the previous triangle, the vectors are added head-to-tail as in Fig. 1.3.

FIGURE 1.3 Vector addition solution to the river problem.

The resultant vector, denoted  , is obtained by filling in the triangle. Mathematically we write  =  + . The graphical method of solving our original problem is to take out a ruler and actually measure the length of the resultant vector . You would  find it to be 50 m.