# u=7i+3j+5k v=-8i+4j+2k determine if the 2 vectors make an acute angle, obtuse angle, or are orthogonal.

u=7i+3j+5k
v=-8i+4j+2k
determine if the 2 vectors make an acute angle, obtuse angle, or are orthogonal.
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Julianna Bell
$u\left(dot\right)v=||u||||v||\mathrm{cos}\theta$.
u(dot)v=<7,3,5>(dot)<-8,4,2>=-56+12+10=-34.
$||u||=\left(49+9+25{\right)}^{1/2}={83}^{1/2},||v||=\left(64+16+4{\right)}^{1/2}={84}^{1/2}$.
$u\left(dot\right)v=||u||||v||\mathrm{cos}\theta$
$-34={6972}^{1/2}\mathrm{cos}\theta$
$34/{6972}^{1/2}=\mathrm{cos}\theta$
$-.407=\mathrm{cos}\theta$
$\mathrm{arccos}\left(-.407\right)=\theta$
114.03 degrees$=\theta .$