`bar(a)=a_(1)hati+a_(2)hatj+a_(3)hatk,bar(b)=b_(1)hati+b_(2)hatj+b_(3)hatk,bar( c )=c_(1)hati+c_(2)hatj+c_(3)hatk` are three non zero vectors. The unit vector `bar( c )` is perpendicular to `bar(a)` and `bar(b)`. The angle between `bar(a)` and `bar(b)` is `(pi)/(6)` then, `|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|` = .............

Options

A. 0
B. 1
C. `(1)/(4)|bar(a)|^(2)|bar(b)|^(2)`
D. `(3)/(4)|bar(a)|^(2)|bar(b)|^(2)`

Answer

C