Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Row reduction of the augmented matrix gives rows $(1,-2,1\mid 3),(0,9,-6\mid -7)$, ( $0,0,0\mid 19$ ), so the system has no solution while the normals are coplanar ( $|A|=0$ ) and no two normals are parallel. The planes form a triangular prism (A true, B false). The direction $(1,2,3)$ is perpendicular to each normal $(1,-2,1),(5,-1,-1),(1,1,-1)$ and $(0,0,0)$ is on none of the planes, so C is true. The point $(r,3r,4r)$ gives $r+3r-4r=0\ne 7$ on the third plane, so that line is parallel to the third plane and never meets it. D is false.