Let a line \( L \) passing through the point \( (1,1,1) \) be perpendicular to both the vectors \( 2\hat{i}+2\hat{j}+\hat{k} \) and \( \hat{i}+2\hat{j}+2\hat{k} \). If \( P(a,b,c) \) is the foot of perpendicular from the origin on the line \( L \), then the value of \( 34(a+b+c) \) is:
