I've come across an exercise that asks the reader to state the correct answer. For me, the only one right is the third, but I would like to know why the first one is not correct also:

The line $r$ is parallel to the plane $\alpha$, but is not contained in it. Choose the correct alternative:

  • The are, in $\alpha$, lines that are perpendicular to $r$

  • All lines in $\alpha$ are parallel to $r$

  • There are, in $\alpha$, lines that are parallel to $r$ and lines that are skew to $r$

  • Line $r$ cannot be coplanar to any line in $\alpha$

  • Every plane that contains $r$ is parallel to $\alpha$

Thank you.


1 Answer 1


Your idea is correct. Regarding the first point, we call two lines perpendicular if they are coplanar ans intersect in a right angle. As the lines in $\alpha$ do not intersect $r$, ...


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