If (\vec{a} = \hat{i} + \hat{j} + \hat{k},\; \vec{b} = 2\hat{i} - \hat{j} + 3\hat{k}) and (\vec{c} = \hat{i} - 2\hat{j} + \hat{k} ) find a unit vector parallel to the vector (2\vec{a} - \vec{b} + 3\vec{c})
(2\vec{a} - \vec{b} + 3\vec{c} = 3\vec{i} - 3\vec{j} + 2\vec{k})
