Question

What is the angle between `<6,3,-6 >` and `<1,7,-3>`?

Answer 1

`theta~=49^o`

Explanation:

`vec A-><6,3,-6>" "vec B-><1,7,-3>`
`"step-1: find ||A|| and ||B||"`
`||A||=sqrt(6^2+3^2+(-6)^2)=sqrt(36+9+36)=sqrt81`
`||B||=sqrt(1^2+7^2+(-3)^2)=sqrt(1+49+9)=sqrt 59`
`"step-2: find dot product "A*B`
`A*B=(6*1)+(3*7)+(-6*-3)=6+21+18=45`
`"step-3: use the formula :" A*B=||A||*||B||*cos theta`

`45=sqrt81*sqrt59*cos theta`
`cos theta=45/(sqrt(81*59))`
`cos theta=45/sqrt4779`
`cos theta=0,6509`
`theta~=49^o`