The two planes $x - 8 y - 9 z = 4$ and $4 x - 21 y - 7 z = - 4$ are parallel.
A)true
B)false

Question

Quizplus · Accepted Answer

Two planes are parallel if their normal vectors are parallel (or proportional). The normal vector of the first plane is $ \langle 1, -8, -9 \rangle $ and for the second plane, it is $ \langle 4, -21, -7 \rangle $. These vectors are not proportional (i.e., the ratios of their corresponding components are not equal: $ 4/1 \neq -21/-8 \neq -7/-9 $), hence the planes are not parallel.

The Two Planes x−8y−9z=4x - 8 y - 9 z = 4x−8y−9z=4

The Two Planes $x - 8 y - 9 z = 4$