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, non - intersecting lines in 3 - D space.

Step2: Analyze each pair

• Pair \(a\) and \(b\):

Line \(a\) and line \(b\) are in the same plane \(M\) (since line \(a\) is perpendicular to line \(d\) and line \(b\) is in plane \(M\) and crosses line \(d\)). They are not skew as they are in the same plane.

• Pair \(c\) and \(b\):

Line \(c\) is in plane \(N\) and line \(b\) is in plane \(M\). They do not intersect and are not parallel.

• Pair \(b\) and \(e\):

Line \(b\) is in plane \(M\) and line \(e\) is in plane \(M\). They are not skew as they are in the same plane.

• Pair \(e\) and \(c\):

Line \(e\) is in plane \(M\) and line \(c\) is in plane \(N\). They do not intersect and are not parallel.

• Pair \(a\) and \(e\):

Line \(a\) and line \(e\) are in the same plane \(M\) (line \(a\) is perpendicular to line \(d\) and line \(e\) is in plane \(M\)). They are not skew as they are in the same plane.

• Pair \(a\) and \(c\):

Line \(a\) is in plane \(M\) and line \(c\) is in plane \(N\). They do not intersect and are not parallel.

Answer:

c and b, e and c, a and c