If \(\vec a = \;\hat i + 2\hat j + 5\hat k\;and\;\vec b = 5\hat i - 4\hat j - 3\hat k\) are two vectors then find the value of \(\left| {\vec a + \;\vec b} \right|\) ?

1
\(\sqrt {17}\)
2
\(\sqrt {44}\)
3
\(\sqrt {13}\)
4
None of these

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