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Proof of the Line-Surface Parallel Determination Theorem

The method to prove that lines and planes are parallel is as follows:

1. Use the definition: prove that there is no common point between a straight line and a plane.

2. Use the decision theorem: From the fact that a straight line is parallel to a straight line, we get that the straight line is parallel to the plane.

3. Use the property of surface parallelism: if two planes are parallel, then the straight line in one plane must be parallel to the other plane.

A straight line and a plane have no common points (do not intersect), and they are said to be parallel to the plane. Theorem of properties of straight lines: If a straight line is parallel to a plane, then the intersection of any plane passing through the straight line and the plane is parallel to the straight line.

4. Space vector method: Prove that the vector of the straight line is perpendicular to the normal vector of the plane, which means that the straight line is parallel to the plane.

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