The volume of the parallelepiped whose coterminous edges are represented by the vectors `2vecb xx vecc, 3vecc xx veca` and `4veca xx vecb` where
`vecb=sin(theta+(2pi)/(3))hati+cos(theta+(2pi)/(3))hatj+sin(2theta+(4pi)/(3))hatk`,
`vecc=sin(theta-(2pi)/(3))hati+cos(theta-(2pi)/(3))hatj + sin(2theta-(4pi)/(3))hatk`
is 18 cubic units, then the values of `theta`, in the interval `(0,pi/2)`, is/are

Options

A. `pi/9`
B. `2pi/9`
C. `pi/3`
D. `4pi/9`

Answer

A, B, D