My book shows three vectors, v, w, and u, which are illustrated geometrically on a plane. Each of them has their own length (magnitude) and direction.

The following operation is performed as an example:

2v + 3w

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Is graphing an accurate depiction of the new magnitude important? If so, I need an explanation of how it is done. My book does not explain how accurate my graph has to be.

Basically, I can figure out the original magnitude of the vector v by using the Pythagorean theorem, but once I multiply it by 2, how do I accurately go about graphing the new magnitude (2v)? Likewise, how would I go about graphing 3w?

Here is a picture of what is in my book, which I've described above:

http://postimage.org/image/uqmaop7bv/

This website is NOT a virus. Just Google postimage.org