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.
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

Answer 1

I can do this, but I need one clarification about the picture: which plane (M or N), if any, does line a lie in, and do c and e meet the intersection line d (and if so, do they meet d at the same point or at different points)?

Why I ask: two lines are skew iff they are not parallel and do not intersect. Useful facts for this configuration:
- Any two lines that both lie in the same plane (both in M or both in N) cannot be skew — they are coplanar and therefore either intersect or are parallel.
- Two lines that lie in different planes M and N can only meet at a point on d (the intersection of the planes). So such a pair is skew exactly when they do not meet on d and are not parallel.

If you tell me:
- whether a lies in M, in N, or is not in either plane,
- whether c and e intersect d (and if so whether at the same point),
I will list exactly which of the six pairs are skew.