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:
