Each of the angle between vectors $\vec a$, $\vec b$ and $\vec c$ is equal to $60^\circ$. If $|\vec a|=4$, $|\vec b|=2$ and $|\vec c|=6$, then the modulus of $\vec a+\vec b+\vec c$ is

$|\vec a+\vec b+\vec c|^2 = a^2+b^2+c^2 +2(\vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a)$ Since angle $=60^\circ$, $\vec a\cdot\vec b=|a||b|\cos60^\circ=\dfrac{ab}{2}$ So, $=16+4+36+2\left(\dfrac{4\cdot2+2\cdot6+6\cdot4}{2}\right)$ $=56+44=100$ $\Rightarrow |\vec a+\vec b+\vec c|=10$