What is the value of linear velocity if $\overrightarrow{\omega }=3\hat{\mathrm{i}}-4\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{r}=5\hat{\mathrm{i}}-6\hat{\mathrm{j}}+6\hat{\mathrm{k}}$?

A particle $P$ is moving in a circle of radius $r$ with a uniform speed $v$. $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$, the angular velocity of $P$ about $A$ and $C$ are in the ratio,