Question

What is the angle between `<-3,5,0 >` and `< 4,0,-2>`?

Answer 1

`alpha~=21^o`

Explanation:

`A= <-3,5,0>" "B= <4,0,-2>`
`"step-1: find the magnitudes:" ||C||=sqrt(a^2+b^2+c^2)`
`||A||=sqrt((-3)^2+5^2+0^2)" "||A||=sqrt36`
`||B||=sqrt(4^2+0^2+(-2)^2)" "||B||=sqrt20`
`"step-2:find dot product of A and B "`
`A.B=(-3*4)+(5*0)+(-2*0)" "A.B=-12`
`"use dot product formula "A.B=||A||*||B||*cos alpha`
`-12=sqrt36*sqrt20*cos alpha`
`-12=sqrt(36*20)*cos alpha`
`cos alpha=-12/sqrt(36*20)`
`cos alpha=-0,93510265`
`alpha~=21^o`