$\displaystyle \begin{array}{{>{\displaystyle}l}} ( d_{1} ;d_{2}) =90^{o} \Rightarrow d_{1} \bot d_{2}\\ \Rightarrow \overrightarrow{n_{d_{1}}} \bot \overrightarrow{n_{d_{2}}}\\ \Rightarrow ( m+3) +2( -m+1) =0\\ \Rightarrow -m+5=0\\ \Rightarrow m=5 \end{array}$