"Magnitude" of a vector is equal to its "length"ifyou are thinking about vectorsgeometrically- say, as "arrows". But there are many other kinds of vectors- for example, the set of all quadratic polynomials forms a vector space. We can define the "magnitude" of such vectors once we have a basis, but it wouldn't really make sense to call it a "length". If I took as basis , then the magnitude of the vector would be

Here, then, they are talking about two different kinds of thing- vectors and line segments. One has a "magnitude", the other a "length". And all that sentence is saying is that youcando what you are doing automatically- representing a vector as a directed line segment.

(I was taken aback for a moment by "hose length" but I think you just dropped the "w"!)