If `bara = a_1 hati + a_2 hatj + a_3 hatk , hatb = b_1 hati + b_2 hatk ` and `barc = c_1 hati + c_2 hatj + c_3 hatk` are non-zero vectors such that `barc` is a unit vector perpendicular to both the vectors ` veca` and `barb` and angle between `bara , barb ` is `pi//6` then, `|{:(a_1 , a_2 ,a_3),(b_1,b_2,b_3),(c_1 , c_2,c_3):}|^2` =

Options

A. 1
B. 0
C. `3/4 (a_1^2 + a_2^2 + a_3^2 )(b_1^2 + b_2^2 + b_3^2)`
D. `1/4 (a_1^2 + a_2^2 + a_3^2) (b_1^2 + b_2^2 +b_3^2) `

Answer

D