If a is perpedicular to b and `c|a| = 2, |b| = 3 |c| = 4` and the angle between b and c is `(2pi)/(3)` , then `[a,b,c]` is equal to

Options

A. `4sqrt3`
B. `6sqrt3`
C. `12sqrt3`
D. `18sqrt3`

Explanation

`:. [(a,b,c)]=a. (bxxc)=a. (|b||c| "sin" (2pi)/3 hat(n))`
`=|b||c| "sin" (2pi)/3 (a.hat(n))`
`=|a||b||c| ("sin" (2pi)/3)`
`[ :' a. hat(n)=|a||hat(n)| cos 0^(@)=|a|]`
`=2xx3xx4xxsqrt(3)/2=12 sqrt(3)`