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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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