If $\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k},|\vec{b}|=5$ and the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{6}$, then the area of the triangle formed by these two vectors as two sides is:

$\frac{15}{2}$ sq. unit $\frac{15 \sqrt{3}}{2}$ sq. unit $\frac{15}{4}$ sq. unit $15 \sqrt{3}$ sq. unit

$\frac{15}{4}$ sq. unit

The correct answer is Option (3) → $\frac{15}{4}$ sq. unit