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Dot product arithmetic

by cytochrome
Tags: arithmetic, product
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cytochrome
#1
Jan14-13, 06:39 PM
P: 162
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)?
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Vorde
#2
Jan14-13, 07:05 PM
Vorde's Avatar
P: 784
Of course, basic algebra.
cytochrome
#3
Jan14-13, 07:09 PM
P: 162
Quote Quote by Vorde View Post
Of course, basic algebra.
Thanks. I didn't know if some weird cosine rule existed in there

Vorde
#4
Jan14-13, 08:07 PM
Vorde's Avatar
P: 784
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}##
chiro
#5
Jan14-13, 10:11 PM
P: 4,577
Hey cytochrome.

If the inner product is valid then all of your statements are true.
xAxis
#6
Jan15-13, 04:23 AM
P: 211
Quote Quote by cytochrome View Post
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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