Question

If `A = <-6 ,2 ,5 >`, `B = <-8 ,3 ,4 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`alpha~=63^o`

Explanation:

`C=(-6-(-8)),(2-3),(5-4)`
`C=<2,-1,1>`
`A*C=A_x*B_x+A_y*B_y+A_z*B_z`
`A*C=-12-2+5=-9`
`||A||=sqrt(36+4+25)" "||A||=sqrt65`
`||C||=sqrt(4+1+1)" "||C||=sqrt6`
`A.C=||A||*||C||*cos alpha`
`-9=sqrt65*sqrt6*cos alpha=`
`-9=sqrt(65*6)*cos alpha`
`-9=sqrt390*cos alpha`
`-9=19,74*cos alpha`
`cos alpha=-9/(19,74)`
`cos alpha=0,445927051672`
`alpha~=63^o`