The plane … is perpendicular to its normal vector … ______

The plane $a_{1}x+b_{1}y+c_{1}z=d_1$ is perpendicular to its normal vector ${\mathbf{N}}_1=$ ______. The plane $a_{2}x+b_{2}y+c_{2}z=d_2$ is perpendicular to ${\mathbf{N}}_2=$ ______. The planes meet in a line that is perpendicular to both vectors, so the line is parallel to their ______ product. If this line is also parallel to the third plane and perpendicular to ${\mathbf{N}}_3$, the system is ______. The matrix has no ______, which happens when $({\mathbf{N}}_1\times {\mathbf{N}}_2)\cdot {\mathbf{N}}_3=0$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.5 Linear Algebra, #10