Question

If `|veca| = 3, |vecb| = sqrt(2)/3` and `veca xx vecb` is a unit vector then the angle between `veca` and `vecb` will be ______.

Options

• `π/6`

• `π/4`

• `π/3`

• `π/2`

Answer 1

If `|veca| = 3, |vecb| = sqrt(2)/3` and `veca xx vecb` is a unit vector then the angle between `veca` and `vecb` will be `underlinebb(π/4)`.

Explanation:

Given `veca xx vecb` is a unit vector,

∴ `|veca xx vecb|` = 1

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

1 = `3 xx sqrt(2)/3 sin θ`

`\implies` sin θ = `1/sqrt(2)`

= `sin  π/4`

`\implies` θ = `π/4`