Vectors along the adjacent sides of parallelogram are `veca = hati +2hatj +hatk and vecb = 2hati + 4hatj +hatk`. Find the length of the longer diagonal of the parallelogram.

Answer

7

Explanation

Vector along the sides are `veca = hati +2hatj +hatk and vecb = 2hati + 4hatj + hatk `
Clearly the vector along the longer diagonal is
`veca + vecb = 3hati +6hatj +2hatk`
Hence, length of the longest diagonal is
`|veca + vecb| = | 3hati +6hatj+2hatk| =7`