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I have a problem with this statement in a Calculus book:

A scalar multiple [tex]s\vec{v}[/tex] of [tex]\vec{v}[/tex] is parallel to [tex]\vec{v}[/tex] with magnitude [tex]|s|\ ||\vec{v}||[/tex] and points in the same direction as [tex]\vec{v} [/tex] if [tex]s>0[/tex], and in the opposite direction if [tex]s<0[/tex]

What bothers me about this statement is it never talks about the origin if they have the same origin then how can they be parallel, there will be multiple intersections. If we take [tex]\vec{v}=\left<2,2\right>[/tex] and [tex]\vec{t}=\left<6,6\right>[/tex] and [tex]s=\frac{1}{3}[/tex] then using the statement above [tex]\vec{v}[/tex] and [tex]\vec{t}[/tex] are parallel if and only if [tex]\vec{v}=s\vec{t}[/tex], which they are but if you graph it in 2 dimensions you can easily see if both vectors origin are the same say 0,0 then they are not parallel.

Are we suppose to assume the origin is never the same, unless explicitly told?

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# Homework Help: Parallel Vectors in R^2

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