Question

If `|veca xx vecb| = sqrt(3)` and `veca.vecb` = – 3, then angle between `veca` and `vecb` is ______.

Options

• `(2π)/3`

• `π/6`

• `π/3`

• `(5π)/6`

Answer 1

If `|veca xx vecb| = sqrt(3)` and `veca.vecb` = – 3, then angle between `veca` and `vecb` is `underlinebb((5π)/6)`.

Explanation:

Given,

`|veca xx vecb| = sqrt(3)` and `veca.vecb` = – 3

Then `|veca||vecb| sin θ = sqrt(3)`  ...(i)

and `|veca||vecb| cos θ` = – 3  ...(ii)

On dividing (i) by (ii), we get

`sinθ/cosθ = sqrt(3)/-3 = (-1)/sqrt(3)`

`\implies` tan θ = `- tan (π/6)`

`\implies` θ = `π - π/6`

= `(5π)/6`