Vector Algebra

The sum of all values of \(\alpha\), for which the points whose position vectors are \(\hat{i}-2 \hat{j}+3 \hat{k}, 2 \hat{i}-3 \hat{j}+4 \hat{k},(\alpha+1) \hat{i}+2 \hat{k}\) and \(9 \hat{i}+(\alpha-8) \hat{j}+6 \hat{k}\) are coplanar, is equal to :