Projective geometry - How to compute a Plücker matrix from a camera center, direction vector and rotation matrix?

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for a homework assignment I am supposed to compute the intersection between two lines in 3D. One of them is defined by the camera center, a direction vector and rotation matrix. Unfortunately, I don't understand how I can get the Plücker matrix line representation from that.

Plücker coordinates are defined as $L = (q, q')$ where $q$ is the direction vector of the line and $q'$ the plane normal (of the plane defined by the origin and the line) as far as I know.

But I have no idea how this would work with the information I have. Could anyone please give me a hint?