$\vec{a},\vec{b},\vec{c}$ are three coplanar unit vectors such that $\vec{a}+\vec{b}+\vec{c}=0.$ If three vectors $\vec{p},\vec{q},and\vec{r}$ are parallel to $\vec{a},\vec{b},and\vec{c},$ respectively, and have integral but different magnitudes, then among the following options, $\left|\vec{p}+\vec{q}+\vec{r}\right|$ can take a value equal to a. $1$ b. $0$ c. $\sqrt{3}$ d. $2$

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