u=7i+3j+5k

v=-8i+4j+2k

determine if the 2 vectors make an acute angle, obtuse angle, or are orthogonal.

v=-8i+4j+2k

determine if the 2 vectors make an acute angle, obtuse angle, or are orthogonal.

ganolrifv9
2022-07-31
Answered

v=-8i+4j+2k

determine if the 2 vectors make an acute angle, obtuse angle, or are orthogonal.

You can still ask an expert for help

Julianna Bell

Answered 2022-08-01
Author has **19** answers

$u(dot)v=||u||||v||\mathrm{cos}\theta $.

u(dot)v=<7,3,5>(dot)<-8,4,2>=-56+12+10=-34.

$||u||=(49+9+25{)}^{1/2}={83}^{1/2},||v||=(64+16+4{)}^{1/2}={84}^{1/2}$.

$u(dot)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}(-.407)=\theta $

114.03 degrees$=\theta .$

u(dot)v=<7,3,5>(dot)<-8,4,2>=-56+12+10=-34.

$||u||=(49+9+25{)}^{1/2}={83}^{1/2},||v||=(64+16+4{)}^{1/2}={84}^{1/2}$.

$u(dot)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}(-.407)=\theta $

114.03 degrees$=\theta .$

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