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Let det A=|{:(l,m,n),(p,q,r),(1,1,1):}| ...

Let det `A=|{:(l,m,n),(p,q,r),(1,1,1):}|` and if `(l-m)^2 + (p-q)^2 =9, (m-n)^2 + (q-r)^2=16, (n-l)^2 +(r-p)^2=25`, then the value `("det." A)^2` equals :

Text Solution

Verified by Experts

The correct Answer is:
4
`det(A)` is twice of area of triangle with vertices `(l,p), (m,q),(n,r)` with sides 3, 4,5
`Delta^(2)=s(s-a)(s-b)(s-c)`
`impliesDelta^(2)=6xx3xx2xx1`
`impliesDelta=6`
Now `det(A)=12`
`impliesdet(B)=144`
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