Let ` vec a=a_1 hat i+a_2 hat j+a_3 hat k , vec b=b_1 hat i+b_2 hat j+b_3 hat k` and `vec c=c_1 hat i+c_2 hat j+c_3 hat k` be three non-zero vectors such that ` vec c` is a unit vector perpendicular to both ` vec a` and `vec b` . If the angle between `a` and `b` is `pi/6,` then prove that `|[a_1,a_2,a_3],[b_1,b_2,b_3],[c_1,c_2,c_3]|^2=1/4(a_1 ^2+a_2 ^2+a_3 ^2)(b_1 ^2+b_2 ^2+b_3 ^2)`