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 vectors, `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

Explanation

`|{:(a_(1) , a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|^(2)= [veca vecb vecc]^(2)`
` = ((veca xx vecb) .vecc)^(2)`
` ( ab sin theta vecc. vecc)^(2)` .
`(a^(2)b^(2))/4`
` 1/4 (a_(1)^(2) + a_(2)^(2)+a_(3)^(2))(b_(1)^(2) =b_(2)^(2) + b_(3)^(2)) `