Vector addition - The first knowledge sharing application in Vietnam

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Suppose that the vector displacement
${\bf r}$ of some point from the origin is specified as follows:

$\begin{displaymath} {\bf r} = {\bf r}_1 + {\bf r}_2. \end{displaymath}$

(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
${\bf r}_1$ , and we then move from point to point along vector ${\bf r}_2$ . The
net result is the same as if we had moved from point directly to point along
vector ${\bf r}$ . Vector ${\bf r}$ is termed the resultant of adding vectors
${\bf r}_1$ and ${\bf r}_2$ .

Figure 12:
Vector addition
$\begin{figure} \epsfysize =2in \centerline{\epsffile{vadd.eps}} \end{figure}$

Note that we have two ways of specifying the vector displacement of point from
the origin: we can either write ${\bf r}_1$ or
${\bf r} - {\bf r}_2$ . The
expression
${\bf r} - {\bf r}_2$ is interpreted as follows: starting at the origin,
move along vector ${\bf r}$ in the direction of the arrow, then move along
vector ${\bf r}_2$ 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.