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in the cube shown below, which lines are intersecting? \\( \\overleftri…

Question

in the cube shown below, which lines are intersecting?
\\( \overleftrightarrow { a e } \\) and \\( \overleftrightarrow { f g } \\)
\\( \overleftrightarrow { a e } \\) and \\( \overleftrightarrow { b f } \\)
\\( \overleftrightarrow { a d } \\) and \\( \overleftrightarrow { e h } \\)
\\( \overleftrightarrow { a b } \\) and \\( \overleftrightarrow { b c } \\)

Explanation:

Step1: Recall the definition of intersecting lines

Intersecting lines are lines that meet at a point.

Step2: Analyze each pair

  • For \(\overleftrightarrow{AE}\) and \(\overleftrightarrow{FG}\): In a cube, \(AE\) and \(FG\) are parallel (not intersecting).
  • For \(\overleftrightarrow{AE}\) and \(\overleftrightarrow{BF}\): \(AE\) and \(BF\) are skew (not in the same plane, not intersecting).
  • For \(\overleftrightarrow{AD}\) and \(\overleftrightarrow{EH}\): \(AD\) and \(EH\) are skew (not in the same plane, not intersecting).
  • For \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{BC}\): \(AB\) and \(BC\) meet at point \(B\) (intersecting).

Answer:

\(\overleftrightarrow{AB}\) and \(\overleftrightarrow{BC}\)