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# If the vectors $p\hat i+\hat j+\hat k,\:\hat i+q\hat j+\hat k,\: \:and\:\:\hat i+\hat j+r\hat k$ $(p\neq q\neq r\neq 1)$ are three coplanar vectors then the value of $pqr-(p+q+r)=?$

$\begin{array}{1 1} -2 \\ -1 \\ 0 \\ 2 \end{array}$

If the given vectors are coplanar then
$\left |\begin {array}{ccc} p & 1 & 1\\1 & q & 1\\1 & 1 & r\end {array}\right|=0$
$\Rightarrow\:pqr-p-r+1+1-q=0$
$\Rightarrow\:pqr-(p+q+r)=-2$