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. `4sqrt(3)`
B. `6sqrt(3)`
C. `12sqrt(3)`
D. `18sqrt(3)`

Answer

C

Explanation

`therefore [a,b,c] = a(|b||c| sin .(2pi)/(3)hatn)`
`=|a||b||c|(sin.(2pi)/(3))`
`[because a hatn =|a||hatn| cos 0^(@) =|a|]`
` = 2xx 3 xx 4 xx (sqrt(3))/(2)`
` = 12 sqrt(2)`