Calculate Velocity of C Rotating About A Axis

[jesuslovesu]

Homework Statement

$$A = (1,1,-2)$$
$$C = (0,1,-5)$$
(in cartesian coordinates)
Let A and C be drawn from a common origin and let C rotate about A with an angular velocity of 2 rad/s. Find the velocity of the head of C.

Homework Equations

$$v = w x r$$

The Attempt at a Solution

w = 2 rad/s
I know I have to take the cross product of w and C (w x C = v) but I am having problems making w as a vector. Initially I thought I would use cylindrical coords and say that it's moving in the phi direction, unfortunately I don't know if that assumption is correct.
Can anyone give me a pointer on how I should begin to write w as a vector?

 

[Nick89]

If by w you mean $\omega$, the angular velocity, then the direction of omega is always perpendicular on the plane of the speed v. Use the right-hand-rule: If you curl your fingers in the direction of v, then the thumb (stretched out) is the direction of omega.

For example, the direction of omega for the hands of a clock (assuming they move with constant speed instead of in little jumps) would be into the clock.

 

[Kurdt]

Omega points along the axis of rotation. It makes sense if you think about what the cross product does and the relation between omega, r and v.