If \(\vec a = \;\hat i + 2\hat j - 3\hat k\;and\;\vec b = 2\hat i + 3\hat j + \hat k\) then find a unit vector in the direction of \({\vec a + \;\vec b}\) ?

• A. \(\frac{3}{{\sqrt {38} }}\;\hat i - \frac{5}{{\sqrt {38}}}\;\hat j - \frac{2}{{\sqrt {38} }}\hat k\)
• B. \(\frac{3}{{\sqrt {38} }}\;\hat i + \frac{5}{{\sqrt {38}}}\;\hat j + \frac{2}{{\sqrt {38} }}\hat k\)
• C. \(\frac{3}{{\sqrt {38} }}\;\hat i + \frac{5}{{\sqrt {38}}}\;\hat j - \frac{2}{{\sqrt {38} }}\hat k\)
• D. None of these