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Q 2203056848. Let `vec(alpha) = a_1 hat(i) + a_2 hat(j) +a_3 hat(k) , vec(beta) = b_1 hat(i) + b_2 hat(j) + b_3 hat(k)` and

`vec(gamma) = c_1 hat(i) + c_2 hat(j) + c_3 hat (k), | vec(alpha) | =2 , vec(alpha)` makes angle `pi/6` with thw

plane of `vec(beta)` and `vec(gamma)` and angle between `vec(beta)` and `vec(gamma)` is `pi/4`, then

`| (a_1, a_2,a_3), (b_1,b_2,b_3), (c_1,c_2,c_3) |` is equal to ( `n` is even natural number)

`( ( |vec(beta) | | vec(gamma) | )^n )/(2^(n/2))`