Plane through Three Non-Collinear Points

An early topic that lends itself well to this sort of exercise is determining the plane determined by three non-collinear points.

Exercise:

1. Find the equation of the plane containing the points (2, 0, 1),   (-1, 2, 3), and (0, 2, -2).
2. Graph this plane along with the three points to verify that all threepoints lie on the plane. To do this, first solve the plane equation for z and graph the plane, entering it in Function 1. Then select Add a Point from the Graph menu, and enter the coordinates of one of the points. Select the default size and colors. (If you wish to vary these settings, be sure the points still show up well in the printout.) Repeat these steps to add the other two points. Rotate the plot to verify that the points lie on the plane and then find a clear view of the plane with the three points on it. Use the Print Graph menu option on the File menu at the top left corner of the applet to print out your resulting view and hand this printout in with this assignment.

Click here to open the CalcPlot3D applet in a new window.

Click here to open a pdf file which contains the instructions for the activity.

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