trig.. angle between two vectors

[vanalm]

My book gave this example, and I must have forgotten how to multiply absolute values or something because I don't see how they got their solution.

Find the smallest positive angle between each pair of vectors:
<-3,2><4,5>

answer:

cos a= (<-3,2>*<4,5>)/(absolute value of <-3,2>*absolulte value of <4,5>

=-2/(square root of 13*square root of 41)

Would someone please show me how to multiply the absolute values? I am not seeing where the square roots come from.

Thanks.

 

[soroban]

Hello, vanalm!

Given a vector: \(\displaystyle \vec{v}\:=\:\langle a,\,b\rangle\)

\(\displaystyle \;\;|\vec{v}|\) means the magnitude (length) of \(\displaystyle \vec{v}\)

And: \(\displaystyle \,|\vec{v}|\;=\;|\langle a,\,b\rangle| \;=\;\sqrt{a^2\,+\,b^2}\)