How do you find the equation of the plane determined by two parameterized lines?

I’m reviewing for my Calc II final tomorrow (ahh!) and my professor published a non-graded packet of review problems…with no answers. So yeah. He gives me two parameterized lines and asks me to find if they intersect and then find the equation for the plane that the two lines determine. Now, in order to check that they intersect, I took the cross product of the vectors implied by the parameterized line equations and saw that it was not zero – this means that the lines will intersect, because the vectors that define their direction are not parallel. However, I’m unsure how to approach finding the plane determined by these parameterized lines. I used the cross product I found as the normal to the plane, but I have two points on the plane to work with (the point you can pull out of each parameterized equation), and I’m not sure which one to put into the component form of the plane equation to determine the correct equation of the plane – I get two different equations depending on which of the points I use.

Any help you can give would be very appreciated!