angle between vectors

[mathstresser]

What is the angle between <4,4,0> and <3,2,-2>?

I know that the angle is equal to inverse cosine ( (a dot b) /the length of a times the lengh of b)

a dot b equals
(4)3+ 4(2)+0(-2)=20
the length of a=4square root of 2
lenght of b= square root of 17

I try inverse cosine (20/(4square-root(34)))

but that doesn't work... what am I doing wrong?

 

[daon]

What is the angle between <4,4,0> and <3,2,-2>?

I know that the angle is equal to inverse cosine ( (a dot b) /the length of a times the lengh of b)

a dot b equals
(4)3+ 4(2)+0(-2)=20
the length of a=4square root of 2
lenght of b= square root of 17

I try inverse cosine (20/(4square-root(34)))

but that doesn't work... what am I doing wrong?

Maybe you inputted into the caluclator incorrectly? I got the same thing as you.

\(\displaystyle \L|<4,4,0>| = \sqrt{16+16+0} = \sqrt{32} = 4 \sqrt{2} \\ |<3,2,-2>| = \sqrt{9+4+4} = \sqrt{17}\\
<4,4,0> \cdot <3,2,-2> = 12 + 8 = 20\\
\theta = cos^{-1}(\frac{20}{4\sqrt{2} \cdot \sqrt{17}}) = cos^{-1}(\frac{5}{\sqrt{34}}) = 0.8575... \,\, or\,\, 30.96^o\)

 

[mathstresser]

I got it now too....

Thank you!