If \overrightarrow{c} is the unit vector in the direction of sum of the vectors \overrightarrow{a}=2 \hat{i}+2 \hat{j}-5 \hat{k} and \overrightarrow{b}=2 \hat{i}+\hat{j}+3 \hat{k}, then |\overrightarrow{c}|=

\frac{4}\sqrt{29} \hat{i}+\frac{3}\sqrt{29} \hat{j}-\frac{2}\sqrt{29} \hat{k}