4. Multiplication of a vector by a scalar





Using a headtotail procedure, a vector v can be added to itself to give the vector v + v. We have v = and v = . It’s natural to write + = as 2v. The vector 2v has length 2v and is in the same direction as v. The notion of multiplication of a vector by a positive integer is then generalised to define the vector sv for all scalars s, as follows.
For example, 3v has three times the magnitude of v but points in the opposite direction; v (also written ) has magnitude and has the same direction as v. Note that 1v has the same magnitude as v but has the opposite direction, and so is the same vector as the negative of v, that is, 1v = v.


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