Question

What is the angle between `<-1,8,8 >` and `<-1,7,3>`?

Answer 1

Angle
`theta=21.8036678^@`
`theta=21^@ 48' 13.2''`

Explanation:

Let the vector `v= -i+8j+8k`
Let the vector `w=-i+7j+3k`
Let `theta` be the angle between the vectors

Use the formula

`cos theta=(v*w)/(|\|v|\|" "|\|w|\|)`

`v*w=(-1)(-1)+8(7)+8(3)=1+56+24=81`

`|\|v|\|=sqrt((-1)^2+8^2+8^2)=sqrt(1+64+64)=sqrt129`

`|\|w|\|=sqrt((-1)^2+7^2+3^2)=sqrt(1+49+9)=sqrt59`

Let us continue

`cos theta=(v*w)/(|\|v|\|" "|\|w|\|)`

`cos theta=(81)/(sqrt129*sqrt59)`

`theta=cos^-1 ((81)/(sqrt129*sqrt59))`

`theta=21.8036678^@`
`theta=21^@ 48' 13.2''`

God bless....I hope the explanation is useful.