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Planes Q and R are parallel. Explain how you know lines a and b are skew.
Planes Q and R are parallel. Line a is on plane Q and is diagonal down and to the left. Line b is on plane R and is diagonal up and to the left.
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Skew lines are lines that do not intersect and are not parallel.
1. They cannot intersect: any intersection point would lie in both plane Q and plane R, but parallel planes do not meet, so no such point exists.
2. They are not parallel: the directions are different (one slopes down-left while the other slopes up-left), so their direction vectors are not scalar multiples.
Since the lines are non‑intersecting and not parallel, they are skew.
1. They cannot intersect: any intersection point would lie in both plane Q and plane R, but parallel planes do not meet, so no such point exists.
2. They are not parallel: the directions are different (one slopes down-left while the other slopes up-left), so their direction vectors are not scalar multiples.
Since the lines are non‑intersecting and not parallel, they are skew.
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