Simple arithmetic(算術) can be also be used for adding vectors if they are in the same direction.

eg.

if a person walks 8 km east one day, and 6 km east the next day, the person will be 8km?+?6km?=?14km eastofthepointoforigin.Wesaythatthenetorresultant?displacement is 14 km to the east (Fig. 3–2a). If, on the other hand, the person walks 8 km east on the first day, and 6 km west (in the reverse direction) on the second day, then the person will end up 2 km from the origin (Fig. 3–2b), so the resultant displacement is 2 km to the east. In this case, the resultant displacement is obtained by subtraction: 8 km?-?6 km?=?2 km.

But simple arithmetic cannot be used if the two vectors are not along the same line. For example, suppose a person walks 10.0 km east and then walks 5.0 km north. These displacements can be represented on a graph in which the positive?y?axis points north and the positive?x?axis points east, Fig. 3–3. On this graph, we?draw an arrow, labeled?D1?, to represent the 10.0-km displacement to the east.?Then we draw a second arrow,?D2?, to represent the 5.0-km displacement to the north. Both vectors are drawn to scale, as in Fig. 3–3.

The resultant displacement is represented by the arrow labeled DR.(The subscript R stands for resultant.)

You can use the Pythagorean theorem only when the vectors are?perpendicular?to each other.

The length of the resultant vector represents its magnitude. Note that vectors can be moved parallel to themselves on paper (maintaining the same length and angle) to accomplish these manipulations. The length of the resultant can be measured with a ruler and compared to the scale. Angles can be measured with a protractor. This method is known as the?tail-to-tip method of adding vectors.

A second way to add two vectors is the?parallelogram method. It is fully equiva- lent to the tail-to-tip method. In this method, the two vectors are drawn starting from a common origin, and a parallelogram is constructed using these two vectors as adjacent sides as shown in Fig. 3–6b. The resultant is the diagonal drawn from the common origin. In Fig. 3–6a, the tail-to-tip method is shown, and we can see that both methods yield the same result.

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