Let ` overset(to)(a) =a_(1) hat(i) + a_(2) hat(j) + a_(3) hat(k) , overset(to)(a) = b_(1) hat(i) +b_(2) hat(j) +b_(3) hat(k) " and " overset(to)(a) = c_(1) hat(i) +c_(2) hat(j) + c_(3) hat(k)` be three non- zero vectors such that `overset(to)(c )` is a unit vectors perpendicular to both the vectors `overset(to)(c )` and `overset(to)(b)`. If the angle between `overset(to)(a) " and " overset(to)(n)` is `(pi)/(6)` then
`|{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}|` is equal to

Options

A. 0
B. 1
C. `(1)/(4)(a_(1)^(2) + a_(2)^(2) + a_(3)^(3))(b_(1)^(2) + b_(2)^(2) + b_(3)^(2))`
D. `(3)/(4) (a_(1)^(2) + a_(2)^(2) + a_(3)^(2))(b_(1)^(2) + b_(2)^(2) + b_(3)^(2)) (c_(1)^(2) + c_(2)^(2) + c_(3)^(2))`

Answer

C