The adjacent sides of parallelogram are $\overrightarrow{\mathrm{a}}=\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}+\widehat{\mathrm{k}}\text{ and }\overrightarrow{\mathrm{b}}=2\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$  . Hence the length of the longer diagonal of the parallelogram is 

Vectors along the sides are  $\overrightarrow{\mathrm{a}}=\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$ and  $\overrightarrow{\mathrm{b}}=2\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$

Clearly the vector along the longer diagonal is $\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}=3\widehat{\mathrm{i}}+6\widehat{\mathrm{j}}+2\widehat{\mathrm{k}}$

Hence, length of the longer diagonal is
$|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}|=|3\widehat{\mathrm{i}}+6\widehat{\mathrm{j}}+2\widehat{\mathrm{k}}|=7$