Prove that the plane 2x + 2y + 4z = 9 is perpendicular to each of the planes x + 2y + 2z – 7 = 0 and 5x + 6y + 7z = 23.

Question

Philoid · Accepted Answer

To show that planes are perpendicular

Where A₁, B₁, C₁ are direction ratios of plane and A₂, B₂, C₂ are of other

plane.

2.1 + 2.2 + 4.2=2 + 4 + 8=14≠0

Hence, planes are not perpendicular.

Similarly for the other plane

2.5 + 2.6 + 2.7=10 + 12 + 14=36≠0

Hence, planes are not perpendicular.