The adjacent sides of parallelogram are a→=i^+2j^+k^ and b→=2i^+4j^+k^  . Hence the length of the longer diagonal of the parallelogram is

Vectors along the sides are  a→=i^+2j^+k^ and  b→=2i^+4j^+k^Clearly the vector along the longer diagonal is a→+b→=3i^+6j^+2k^Hence, length of the longer diagonal is|a→+b→|=|3i^+6j^+2k^|=7