Question

parallel lines a and b lie in the y plane through the a line, the alpha a plane is drawn through beta so that alpha and beta intersect along the ac line.Prove that ac is parallel to y



параллельные прямые а и б лежат в плоскости y через прямую а проведена плоскость альфа а через бета так,что альфа и бета пересекаются по прямой ac.Докажите,что ac паралельно y

Answer 1

To prove that line ac is parallel to the y-plane, you can follow these steps:

1. Since lines a and b are in the y-plane and line a lies in the y-plane, it means lines a and b are parallel.

2. Now, the alpha plane is drawn through beta, so alpha and beta intersect along the ac line.

3. If lines alpha and beta intersect along line ac, it implies that line ac is in the alpha plane.

4. Since lines a and b are parallel and ac is in the alpha plane, we can conclude that ac is also parallel to lines a and b.

5. Therefore, ac is parallel to the y-plane (since lines a and b are in the y-plane), and this completes the proof.

So, the line ac is indeed parallel to the y-plane based on the given conditions.