# Dot product arithmetic

1. ### cytochrome

163
If you square the magnitude of a vector you get the dot product, correct?

||v||^2 = v . v

Can you also say that

||v|| = sqrt(v . v)?

Last edited: Jan 14, 2013
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3. ### Vorde

784
Of course, basic algebra.

4. ### cytochrome

163
Thanks. I didn't know if some weird cosine rule existed in there

5. ### Vorde

784
Okay. Just to cement this:

If ##\vec{v} = <a,b>## and ##\vec{w} = <c,d>## then ##\vec{v} \cdot \vec{w} = ac+bd## and ##\vec{v} \cdot \vec{v} = a^2+b^2##

So if ##|| \vec{v} || ^2 = \vec{v} \cdot \vec{v} = a^2+b^2## then ##\sqrt{|| \vec{v} || ^2} = || \vec{v} || = \sqrt{a^2+b^2}##

6. ### chiro

Hey cytochrome.

If the inner product is valid then all of your statements are true.

7. ### xAxis

214
cosine rule cannot bother you here because the angle between "vectors" is zero.