$\vec a$$\vec b$ = $\left\vert\vec a\right\vert$ $\left\vert\vec b\right\vert$
                             = $(2)(1)$$\cos 60^\circ$
                             = $1$
$\vec a$+$\vec b$+$\vec c$ = $0$
$\vec a$+$\vec b$ = -$\vec c$
${\left\vert\vec a+\vec b\right\vert}^2$ = ${\left\vert-\vec c\right\vert}^2$
${\left\vert\vec a\right\vert}^2$ + $2$($\vec a$$\vec b$) + ${\left\vert\vec b\right\vert}^2$ = ${\left\vert\vec c\right\vert}^2$
$2^2$+$2$$(1)$+$1^2$ = ${\left\vert\vec c\right\vert}^2$
$7$ = ${\left\vert\vec c\right\vert}^2$
 $\left\vert\vec c\right\vert$ = $\sqrt{7}$
จาก $\left\vert\vec a\right\vert$ = $2$, $\left\vert\vec b\right\vert$ = $1$, $\left\vert\vec c\right\vert$ = $\sqrt{7}$  
$\vec a$+$\vec b$+$\vec c$ = $0$
$\vec b$+$\vec c$ = $-\vec a$
${\left\vert\vec b+\vec c\right\vert}^2$ = ${\left\vert-\vec a\right\vert}^2$
${\left\vert\vec b\right\vert}^2$ + $2$($\vec b$$\vec c$) + ${\left\vert\vec c\right\vert}^2$ = ${\left\vert\vec a\right\vert}^2$
$1^2$+$2$($\vec a\vec c$)+$(\sqrt{7})^2$ = $2^2$
$2$($\vec b\vec c$) + $8$ = $4$
$\vec b\vec c$ = -$2$
$\vec b\vec c$ = $\left\vert\vec b\right\vert$$\left\vert\vec c\right\vert$$\cos \theta$
-$2$ = $(1)$($\sqrt{7}$)$\cos\theta$
$\cos\theta$ = $\frac{-2}{\sqrt{7}}$
$\theta$ = $arc (cos \frac{-2}{\sqrt{7}})$
$\theta$ = $\pi$ - $arc (cos \frac{2}{\sqrt{7}})$
จาก $arc (cos \frac{2}{\sqrt{7}})$ = $arc (sin x)$
$x$ = $sin$($arc (cos \frac{2}{\sqrt{7}})$)
$x$ = $\sqrt{\frac{3}{7}}$
ดังนั้น $\theta$ = $\pi$-$arc sin\sqrt{\frac{3}{7}}$