1.

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(k)andvec(c)=c_(1)hat(i)+c_(2)hat(j)+c_(3)hat(k) be three non-zero vectors such that vec(c) is a unit vector perpendicular to both vec(a)andvec(b). If the angle between vec(a)andvec(b)" is "(pi)/(6), then {:""|(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|"":}^(2)" is equal to"

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`(1)/(4)(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))`
`(3)/(4)(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))(c_(1)^(2)+c_(2)^(2)+c_(3)^(2))`

Answer :C


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