show that the two lines x=(-1/2 t, 2/3 t +1, t- 3/2) and x= (t- 3/2, 2t+3, 3t+ 9/2) intersect. find an equation for the plane that they determine.

i have no clue how to do this i keep getting stuck.. the professor's hint was:

Part (1): show that the given lines intersect. In order to do this, you should rename one of the variables given in the expressions for these lines. The book writes both lines using the same variable, t. In order to find out where these two lines meet, you need to first rename the variable in the second line, say, to s. Then set the two expressions equal which sets the three vector components equal and then solve the system of equations that results. You will find a value for t and a value for s. Plugging these values in to their respective lines produces (or should produce, if your math is correct) the same point -- the point of intersection.

Part (2) then asks you to find the equation of a plane containing these intersecting lines, which I think you can do without a hint

anyone want to start me off? i changed the variables in the second equation to s's, but what do i set equal? the entire equations or just the x's, y's, and z's? i'm so lost