Question

examining lines in three dimensions. planes m and n intersect at line d. line a forms a right angle with line d. line b is diagonal and crosses line d. line c is on plane n and is diagonal. line e is on plane m and is slightly diagonal at the top of the plane. which are skew lines? check all that apply. a and b c and b b and e e and c a and e a and c

Explanation:

Step1: Recall skew - lines definition

Skew lines are non - parallel and non - intersecting lines in 3 - D space.

Step2: Analyze line pairs

• a and b: Line a and line b intersect at the intersection of planes M and N (since b crosses line d and a is perpendicular to d), so they are not skew.
• c and b: Line c and line b intersect at a point on line d (as b crosses line d and c is on plane N which intersects M at d), so they are not skew.
• b and e: Line b is on plane N and line e is on plane M. They are non - parallel and do not intersect, so they are skew.
• e and c: Line e is on plane M and line c is on plane N. They are non - parallel and do not intersect, so they are skew.
• a and e: Line a and line e are on the same plane M, so they are not skew.
• a and c: Line a is perpendicular to line d and line c is on plane N. They are non - parallel and do not intersect, so they are skew.

Answer:

b and e, e and c, a and c