Let `veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk` gve 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 prove that `|{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|p=1/4 (a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))`

Explanation

To prove the given statement, we start with the vectors defined in the question:

Let:
\[ \vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} \]
\[
\vec{b} = b_2 \hat{j} + b_3 \hat{k}
...