C4.4

recognize a scalar equation for a plane in three-space to be an equation of the form $Ax+By+Cz+D=0$ whose solution points make up the plane, determine the intersection of three planes represented using scalar equations by solving a system of three linear equations in three unknowns algebraically (e.g., by using elimination or substitution), and make connections between the algebraic solution and the geometric configuration of the three planes Sample problem: Determine the equation of a plane $P_3$ that intersects the planes $P_1$, $x+y+z=1$, and $P_2$, $x-y+z=0$, in a single point. Determine the equation of a plane $P_4$ that intersects $P_1$ and $P_2$ in more than one point.