Let `veca=a_(1)hati+a_(2)hatj+a_(3)hatk, vecb=b_(1)hati+b_(2)hatj+b_(3)hatk` and `vecc=c_(1)hati+c_(2)hatj+c_(3)hatk` be three non zero vectors such that `vecc` is a unit vector perpendicular to both `veca` and `vecb` . If the angle between `veca` and `vecb` is `(pi)/6`, then `|(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|^(2)` is equal to

Options

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

Answer

C