Students: The attached geogebra rendering shows the intersection of 3 planes with cartesian equations a_i*x + b_i*y + c_i*z = d_i for i = 1, 2, 3.
Explore different values for the coefficients and investigate: 1. Under what conditions is the intersection of 3 planes a point, a line, a plane, the empty set? 2. How many different cases can you identify? 3. How can you use the coefficients of the Cartesian equations of the planes to identify each case?