###### Exploration 5.2.1

a. Find the equation of the plane containing the points \((2, 0, 1)\text{,}\) \((-1, 2, 3)\text{,}\) and \((0, 2, -2)\text{.}\)

b. Graph this plane along with the three points to verify that all three points lie on the plane. To do this, first solve the plane equation for \(z\) and graph the plane, entering it in the provided function box on the left. To see its graph, either press enter on the function or click the *Graph* button. Just above this function there should be a dropdown menu labeled: *Add to graph*. Select to *add a Point (x, y, z)*, entering the coordinates of one of the points. You can use the default size and colors. (If you wish to vary these settings, be sure the points still show up well in the printout.) Note that the checkbox to the left of a function, point, or other object needs to be selected if you wish to see that object in the plot.

Repeat these steps to add the other two points. Rotate the plot to verify that all the points lie on the plane and then find a clear view of the plane with the three points on it. Use the *Print Plot* menu option on the *File* menu at the top left corner of the CalcPlot3D app to print out your resulting view and hand this printout in with this assignment.

Answer: The plane equation is: \(z = (22 – 10x – 13y)/2\)