Chapter 6.5, Problem 261E

For the following exercises, consider a rigid body that is rotating about the x-axis counterclockwise with constant angular velocity $\omega =\langle a,b,c\rangle$ . If $P$ is a point in the body located at $r=x\text{i}+y\text{j}+z\text{k}$ , the velocity at $P$ is given by vector field $\text{F = }\omega \times \text{ r}$ .

261. Express $\text{F}$ in terms of $\text{i}$ , $\text{j}$ , and $\text{k}$ vectors.