Question

Find the angle between the vectors `2hat"i" - hat"j" + hat"k"` and `3hat"i" + 4hat"j" - hat"k"`.

Answer 1

Let `2hat"i" - hat"j" + hat"k"` and `3hat"i" + 4hat"j" - hat"k"`

And let θ be the angle between `vec"a"` and `vec"b"`.

∴ cos θ = `(vec"a" * vec"b")/(|vec"a"||vec"b"|)`

= `((2hat"i" - hat"j" + hat"k")*(3hat"i" + 4hat"j" - hat"k"))/(sqrt(4 + 1 + 1) * sqrt(9 + 16 - 1))`

= `(6 - 4 - 1)/(sqrt(6) * sqrt(26))`

⇒ `1/(2sqrt(3) * sqrt(13)) = 1/(2sqrt(39))`

∴ θ = `cos^-1  1/(2sqrt(39))`

⇒ θ = `cos^-1 (1/156)`

Hence, the required value of θ is `cos^-1 (1/156)`.