The altitude of a parallelepiped whose three coterminous edges are vectors \( \vec{A} = \hat{i} + \hat{j} + \hat{k} ‚ \vec{B} = 2 \hat{i} + 4 \hat{j} − \hat{k} \quad\text{and}\quad \vec{C} = \hat{1} + \hat{j} + 3 \hat{k} , w i t h \vec{A} \quad\text{and}\quad \vec{B} \) as sides of the base of the parallelepiped is-

A \( \frac{4 √ 3}{5} \)

B \( \frac{4 √ 31}{7} \)

C \( \frac{2 √ 38}{19} \)