Dot product arithmetic

by cytochrome
Tags: arithmetic, product
 P: 145 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)?
 P: 781 Of course, basic algebra.
P: 145
 Quote by Vorde Of course, basic algebra.
Thanks. I didn't know if some weird cosine rule existed in there

P: 781

Dot product arithmetic

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}##
 P: 4,542 Hey cytochrome. If the inner product is valid then all of your statements are true.
P: 184
 Quote by cytochrome Thanks. I didn't know if some weird cosine rule existed in there
cosine rule cannot bother you here because the angle between "vectors" is zero.

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