Determine the vector and parametric equations

[Styx]

Determine the vector and parametric equations of the plane that contains point C(1,-2,6) and the z-axis

I take this to mean that any point on the z-axis is valid so does that mean either (0, 0, 1) or (1, -2, 5) are also on the plane?

 

[pizzasky]

You are right in saying that the points (0, 0, 1) and (1, -2, 5) are on the plane.

However, can you see that the point (0, 0, 0) is also on the plane? (You don't really need to know this to solve your question, but I thought it would be nice if you are aware of this fact)