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Let a=a_(1)hati+a_(3)hatk, b=b_(1)hati+b_(3)hatk, c=c_(1)hati+c_(2)hatj+c_(3)hatk. If |c|=1 and (axxb)xxc=0, then |(a_(1),a_(2),a_(2)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|is equal to

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`|a|^(2)|b|^(2)`
`|AXXB|^(2)`

Solution :GIVEN, `(axxb)xxc=0, " then " c = (axxb)/(|axxb|) `
`therefore (a xxb)*c = |axxb| `
`RARR |(a_(1),a_(2),a_(3)),(b_(1),b_(2), b_(3)),(c_(1),c_(2),c_(3))|=|axxb|^(2)`


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