The head-to-tail method involves drawing a vector to scale on a sheet of paper beginning at a designated starting position. Where the head of this first vector ends, the tail of the second vector begins (thus, *head-to-tail* method). The process is repeated for all vectors that are being added. Once all the vectors have been added head-to-tail, the resultant is then drawn from the tail of the first vector to the head of the last vector; i.e., from start to finish. Once the resultant is drawn, its length can be measured and converted to *real* units using the given scale. The direction of the resultant can be determined by using a protractor and measuring its counterclockwise angle of rotation from due East.

A step-by-step method for applying the head-to-tail method to determine the sum of two or more vectors is given below.

- Choose a scale and indicate it on a sheet of paper. The best choice of scale is one that will result in a diagram that is as large as possible, yet fits on the sheet of paper.
- Pick a starting location and draw the first vector
*to scale *in the indicated direction. Label the magnitude and direction of the scale on the diagram (e.g., SCALE: 1 cm = 20 m). - Starting from where the head of the first vector ends, draw the second vector
*to scale* in the indicated direction. Label the magnitude and direction of this vector on the diagram. - Repeat steps 2 and 3 for all vectors that are to be added
- Draw the resultant from the tail of the first vector to the head of the last vector. Label this vector as
**Resultant** or simply **R**. - Using a ruler, measure the length of the resultant and determine its magnitude by converting to real units using the scale (4.4 cm x 20 m/1 cm = 88 m).
- Measure the direction of the resultant using the counterclockwise convention.

An example of the use of the head-to-tail method is illustrated below. The problem involves the addition of three vectors:

### 20 m, 45 deg. + 25 m, 300 deg. + 15 m, 210 deg.

### SCALE: 1 cm = 5 m