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Suppose that
. This expression is interpreted as
follows: vector points in the same direction as vector , but
the length of the former vector is times that of the latter. Note
that if is negative then vector points in the opposite direction to
vector , and
the length of the former vector is times that of the latter. In terms
of components:

(37) 
In other words, when we multiply a vector by a scalar then the components of the resultant
vector are obtained
by multiplying all the components of the original vector by the scalar.
Richard Fitzpatrick
20060202