Question

If the angle between `veca` and `vecb` is `π/3` and `|veca xx vecb| = 3sqrt(3)`, then the value of `veca.vecb` is ______.

Options

• 9

• 3

• `1/9`

• `1/3`

Answer 1

If the angle between `veca` and `vecb` is `π/3` and `|veca xx vecb| = 3sqrt(3)`, then the value of `veca.vecb` is 3.

Explanation:

∵ `veca xx vecb = |veca|.|vecb| sin θ`

`\implies |veca|.|vecb| sin  π/3 = 3sqrt(3)`  ...`[∵ θ = π/3]`

`\implies |veca|.|vecb|. sqrt(3)/2 = 3sqrt(3)`

`\implies |veca|.|vecb|` = 6  ...(i)

Now `veca.vecb = |veca|.|vecb| cos θ`

`veca.vecb = 6 . cos  π/3`  ...[From (i)]

= `6 . 1/2`

`veca.vecb` = 3.