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Let vec a=a1 hat i+a2 hat j+a3 hat k , ...

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 ka n d vec c=c_1 hat i+c_2 hat j+c_3 hat k` be three nonzero vectors such that ` vec c` is a unit vector perpendicular to both ` vec aa n d vec bdot` If the angle between ` vec aa n d vec b` is `pi//6` , then the value of `|a_1b_1c_1a_2b_2c_2a_3b_3c_3|^2` is a.`0` b. `1` c. `1/4(a1^2+a2^2+a3^2)(b1^2+b2^2+b3^2)` d. `3/4(a1^2+a2^2+a3^2)(b1^2+b2^2+b3^2)`

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