Vector addition
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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 .
Figure 12:
Vector addition
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