The non-zero vectors $\vec{a},\vec{b}$ and $\vec{c}$ are related by $\vec{a}=8\vec{b}$ and $\vec{c}=-7\vec{b}$. Then the angle between $\vec{a}$ and $\vec{c}$ is:

We are given $\vec{a}=8\vec{b}$ and $\vec{c}=-7\vec{b}$.This means $\vec{a}$ is in the same direction as $\vec{b}$ (since $8>0$).And $\vec{c}$ is in the opposite direction to $\vec{b}$ (since $-7<0$).Therefore, $\vec{a}$ and $\vec{c}$ are in opposite directions.The angle between two vectors in opposite directions is $\pi$ ($180^{\circ }$).