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Let `veca=a_1hati+a_2hatj+a_3hatk, vecb=b_1hati+b_2hatj+b_3hatk`, and `vecc=c_1hati+c_2hatj+c_3hatk` be three non-zero vectors such that c is a unit vector perpendicular to both `veca`and `vecb` if angle between `veca`and`vecb` is `pi/3`, then the value of `|[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|^2` is:
A. |
0 |
B. |
`3/4|veca|^2 |vecb|^2` |
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C. |
`|veca|^2 |vecb|^2` |
D. |
none of these |