Question

Find the angle between two vectors `veca` and `vecb` with magnitudes `sqrt3` and 2, respectively having `veca.vecb = sqrt6`.

Answer 1

Let θ be the angle between `veca, vecb` then,

cosθ = `(veca xx vecb)/(|veca||vecb|)`

∵ `veca xx vecb = sqrt6, |veca| = sqrt3, |vecb| = 2`

`∴ cosθ = sqrt6/((sqrt3)(2))`

`= ((sqrt3)(sqrt2))/((sqrt3)(2)`

`= 1/sqrt2   `

`= cos  pi/4`

∴ `theta = pi/4`

Hence, the angle between the given vectors `vec(a) and vec(b)  "is" pi / 4 .`