Question

Identify which of the following sets of planes in three- dimension space are parallel and state the reasoning

A.x=4 y=4
B. x+z=8 y-z=8
C. x+y-z=-1 -x-y+z=1
D. 3x-2y+6z=0
E. -9x+6y-18z=0

Answer 1

The sets of parallel planes in three-dimensional space are A and C.

Step-by-step explanation:

First, let's analyze each set of plane equations to determine if they are parallel:

• A. The equations x=4 and y=4 represent parallel planes that are parallel to the x and y axes, respectively.
• B. The equations x+z=8 and y-z=8 represent planes that are not parallel to each other or to any of the coordinate axes. Therefore, they are not parallel.
• C. The equations x+y-z=-1 and -x-y+z=1 represent planes that are parallel to each other and to the xy-plane.
• D. The equation 3x-2y+6z=0 represents a plane that is not parallel to any of the coordinate axes.
• E. The equation -9x+6y-18z=0 represents a plane that is not parallel to any of the coordinate axes.

Based on this analysis, the sets of planes that are parallel are A and C.