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Suppose that the vector displacement of some point from the origin is specified as follows:
 (31)

Figure 12 illustrates how this expression is interpreted diagrammatically: in order to get from point to point , we first move from point to point along vector , and we then move from point to point along vector . The net result is the same as if we had moved from point directly to point along vector . Vector is termed the resultant of adding vectors and .

Note that we have two ways of specifying the vector displacement of point from the origin: we can either write or . The expression is interpreted as follows: starting at the origin, move along vector in the direction of the arrow, then move along vector in the opposite direction to the arrow. In other words, a minus sign in front of a vector indicates that we should move along that vector in the opposite direction to its arrow.

Suppose that the components of vectors and are and , respectively. As is easily demonstrated, the components of the resultant vector are

 (32) (33) (34)

In other words, the components of the sum of two vectors are simply the algebraic sums of the components of the individual vectors.

Next: Vector magnitude Up: Motion in 3 dimensions Previous: Vector displacement
Richard Fitzpatrick 2006-02-02