Question

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 the definition of skew lines

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

Step2: Analyze each pair

• a and b: Intersect at a point (where line \(a\) and line \(b\) cross on plane \(M\)), so not skew.
• c and b: Line \(c\) is on plane \(N\), line \(b\) is not on plane \(N\), they are non - parallel and non - intersecting.
• b and e: Line \(b\) is not on plane \(M\) (where line \(e\) is), non - parallel and non - intersecting.
• e and c: Line \(e\) is on plane \(M\), line \(c\) is on plane \(N\), but they are parallel (by the orientation in the figure, assume correct based on skew - line criteria checking), so not skew.
• a and e: Intersect at a point (in the 3 - D structure, assume intersection based on plane and line positions), so not skew.
• a and c: Line \(a\) is perpendicular to line \(d\) (plane \(M\) and \(N\) intersection), line \(c\) is on plane \(N\), non - parallel and non - intersecting.

Answer:

c and b, b and e, a and c