Question

A. "Which line is parallel to line CF?"

b. "Which line is perpendicular to line AB?"
c. "Which line is skew to line AH?"
d. "Which plane is parallel to plane AHG?"

Answer 1

To determine parallel and perpendicular lines, we must analyze their orientation relative to each other and to the coordinate axes. Lines that are skew do not intersect and are not parallel. Identifying parallel planes involves recognizing planes that share the same orientation but are at different positions in space.

Step-by-step explanation:

To answer the questions provided by the student, we need to utilize our understanding of geometry, specifically in relation to lines, planes, and vectors within a coordinate system.

1. For the first question, 'Which line is parallel to line CF?', since all three given lines are along the x-axis and parallel to each other, any of them could be a possible option depending on the specific context provided.
2. In response to 'Which line is perpendicular to line AB?', we look for lines that are mutually perpendicular to AB. This could be any line that forms a 90-degree angle with AB in the coordinate system.
3. When considering 'Which line is skew to line AH?', we need a line that does not intersect with AH and is not in a plane parallel to AH. This could be any line that is not coplanar with AH and does not intersect it.
4. Lastly, 'Which plane is parallel to plane AHG?' requires us to identify a plane that does not intersect with plane AHG but runs in the same direction. This would be a plane that shares a similar orientation but is displaced along the axis perpendicular to both planes.