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which rays are part of line be? o \\( \\overrightarrow { a c } \\) and …

Question

which rays are part of line be?
o \\( \overrightarrow { a c } \\) and \\( \overrightarrow { a e } \\)
o \\( \overrightarrow { a b } \\) and \\( \overrightarrow { a e } \\)
o \\( \overrightarrow { a c } \\) and \\( \overrightarrow { a b } \\)
o \\( \overrightarrow { a b } \\) and \\( \overrightarrow { a f } \\)

Explanation:

Step1: Recall the definition of a ray

A ray has one endpoint and extends infinitely in one direction. A line has no endpoints and extends infinitely in both directions. A line can be thought of as being composed of two opposite - direction rays with the same initial point.

Step2: Analyze the line \(BE\)

The line \(BE\) passes through points \(B\) and \(E\) (with \(A\) on the line \(BE\)). The ray \(\overrightarrow{AB}\) starts at \(A\) and goes through \(B\) (in the direction away from \(E\)), and the ray \(\overrightarrow{AE}\) starts at \(A\) and goes through \(E\) (in the direction away from \(B\)). Together, \(\overrightarrow{AB}\) and \(\overrightarrow{AE}\) make up the line \(BE\) (since a line is the union of two opposite - direction rays with the same initial point).

  • For \(\overrightarrow{AC}\) and \(\overrightarrow{AE}\): \(\overrightarrow{AC}\) is not on the line \(BE\).
  • For \(\overrightarrow{AC}\) and \(\overrightarrow{AB}\): \(\overrightarrow{AC}\) is not on the line \(BE\).
  • For \(\overrightarrow{AB}\) and \(\overrightarrow{AF}\): \(\overrightarrow{AF}\) is not on the line \(BE\).

Answer:

\(\overrightarrow{AB}\) and \(\overrightarrow{AE}\) (the second option: \(\bigcirc\overrightarrow{AB}\) and \(\overrightarrow{AE}\))