1. At what point does the line with equation (x,y,z) = (12, -5, -4) +t(3, -4, -2),t , intersect thexy-plane?

2. Consider a system comprised of a line and plane in ³. Question 1 above shows us that such a system can have one solution. How many distinct arrangements are there for a system made up of one line and one plane? (I.e., Is it possible for there to be exactly two solutions? Three solutions? etc.).

a.) Draw diagrams to show the different cases that are possible for a system made of up ofone line andone plane in ³. Be sure to indicatehow many solutions there are for each case.

b.) In Question 1 of the Knowledge section you found the Cartesian equation of a plane that contained the line (x,y,z) = (1, -2, 3) +t(4, 3, -5),t . Consider asystem made up of this line and your Cartesian equation. Under which case would this system be in your answer to 2(a) above?

c.) Verify your Cartesian equation from Question 1 of the Knowledge section by proving that the line

(x,y,z) = (1, -2, 3) +t(4, 3, -5),t , does indeed lie on the plane with your Cartesian equation.