Question

Find the angle between the vectors

`hat"i" - hat"j"` and `hat"j" - hat"k"`

Answer 1

Let θ be the angle between the given vectors, then

cos θ = `((hat"i" - hat"j") (hat"j" - hat"k"))/(|hat"i" - hat"j"| |hat"j" - hat"k"|)`

= `((hat"i" - hat"j" + 0hat"k")(0hat"i" + hat"j" - hat"k"))/(|hat"i" - hat"j"| |hat"j" - hat"k"|)`

= `((1)(0) + (-1)(1) + (0)(-1))/(sqrt(1^2 + (-1)^2 + 0^2) sqrt(0^2 + (1)^2 + (-1)^2`

= `(0 - 1 + 0)/(sqrt(1 + 1 - 0) sqrt(0 + 1 + 1)`

= `(-1)/(sqrt(2)*sqrt(2)`

cos θ = `-1/2`

cos θ = `- cos(pi/3) = cos(pi - pi/3)`

cos θ = `cos((3pi - pi)/3) = cos  (2pi)/3`

 θ = `(2pi)/3`