Question

Find the angle between the vectors

`2hat"i" + 3hat"j" - 6hat"k"` and `6hat"i" - 3hat"j" + 2hat"k"`

Answer 1

Let θ be the angle between the given vectors, then

cos θ = `((2hat"i" + 3hat"j" - 6hat"k") * (6hat"i" - 3hat"j" + 2hat"k"))/(|2hat"i" + 3hat"j" - 6hat"k"| |6hat"i" - 3hat"j" + 2hat"k"|)`

= `((2)(6) + (3)(- 3) + (- 6)(2))/(sqrt(2^2 + 3^2 + (- 6)^2) sqrt(6^2 + (- 3)^2 + 2^2)`

= `(12 - 9 - 12)/(sqrt(4 + 9 + 36) sqrt(36 + 9 + 4)``

= `(- 9)/(sqrt(49) * sqrt(49)`

= `( - 9)/49`

θ = `cos^-1 ((-9)/49)`