Solve this following
Question:

If $\vec{a}, \vec{b}$, and $\vec{c}$ are unit vectors such that $\vec{a}+2 \vec{b}+2 \vec{c}=\overrightarrow{0}$, then $|\vec{a} \times \vec{c}|$ is equal to :

1. $\frac{1}{4}$

2. $\frac{\sqrt{15}}{16}$

3. $\frac{15}{16}$

4. $\frac{\sqrt{15}}{4}$

Correct Option: , 4

Solution: