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Let a vector vec(a) be coplanar with vec...

Let a vector `vec(a)` be coplanar with vectors `vec(b) = 2hat(i) + hat(j) + hat(k)` and `vec(c) = hat(i) - hat(j) + hat(k)`. If `vec(a)` is perpendicular to `vec(d) = 3hat(i) + 2hat(j) + 6hat(k)`, and `|vec(a)| = sqrt(10)`. Then a possible value of `[[vec(a),vec(b),vec(c)]] + [[vec(a), vec(b), vec(d)]] + [[vec(a),vec(c),vec(d)]]` is equal to :

A

`-42`

B

`-40`

C

`-29`

D

`-38`

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