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High school mathematics proves whether the parallel plane of a straight line can be proved to be parallel to the normal vector of the plane perpendicular to the straight line.
The basic method to solve the problem:

1) In solid geometry, select appropriate points and straight line directions, and establish a spatial rectangular coordinate system.

2) If the coordinate calculation unit is not given in the question, you can choose the appropriate line segment to set the length unit;

3) Calculate the coordinate values of relevant points and find out the coordinates of relevant vectors;

4) Solve a given problem

The way to prove that a straight line is perpendicular to a plane is to select two vectors in the plane and multiply them with the known straight line vectors respectively. As long as it is zero, the conclusion can be explained.

The key to prove that a straight line is parallel to a plane is to find a vector parallel to the vector of the straight line in the plane. This turns into a problem of proving that two vectors are parallel, as long as one of them is m (real number) times of the other.