Question

If `A = <8 ,1 ,-5 >`, `B = <6 ,5 ,-8 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`theta=93.366^@`

Explanation:

`vec A=<8,1-5>` => `|vec A|=sqrt(64+1+25)=sqrt(90)=3sqrt(10)`
`vec B=<6,5,-8>`
`vec C=vec A - vec B=<8-6,1-5,-5+8> =<2,-4,3>`
`-> \vec C|=sqrt(4+16+9)=sqrt(29)`

`vecA*vecC=|vec A||vec C|*cos theta`
`cos theta=(vec A*vec C)/(|vec A||vec C|)=(8*2+1(-4)+(-5)(3))/(3sqrt(10)*sqrt(29))=(16-4-15)/(3sqrt(290))=-3/(3sqrt(290))=-1/sqrt(290)` `-> theta=93.366^@`