Question

What is the angle between `<-4,0,-2 >` and `< -2,-1,4 >`?

Answer 1

`pi/2`

Explanation:

Angle between two vectors is given by the formula
`cos theta= (u.v)/(||u|| ||v||`

Dot product u.v in this case is (-4)(-2)+(0)(-1) +(-2)(4)=0.

`||u||= sqrt (16+4)= sqrt20` and ||v||= `sqrt(4+1+16)=sqrt21`

Thus `cos theta =0/sqrt420 =0`

Hence `theta = pi/2`