\overrightarrow{D_1A_1}=\overrightarrow{D_1D}+\overrightarrow{DA_1}=-\frac{a\overrightarrow{DA}+b\overrightarrow{DB}+c\overrightarrow{DC}}{a+b+c}-\frac{b\overrightarrow{DB}+c\overrightarrow{DC}}a=-\frac{a^2\overrightarrow{DA}+b(2a+b+c)\overrightarrow{DB}+c(2a+b+c)\overrightarrow{DC}}{a(a+b+c)}