1, vertical line:
(1) If Line A is perpendicular to Line B and Line B//C, Line A is perpendicular to Line C..
(2) If a straight line is perpendicular to a plane, then this straight line is perpendicular to all the straight lines in the plane.
2. Line-plane verticality: a straight line is perpendicular to two non-parallel straight lines in the plane.
3. Parallel lines:
(1) If two lines are parallel to the third line at the same time, the two lines are parallel.
(2) If two straight lines are perpendicular to the same plane at the same time, the two straight lines are parallel.
4. Line-plane parallelism: If a straight line out of the plane is parallel to a straight line in the plane, the straight line is parallel to the plane.
5. Face-to-face verticality: Let the intersection of plane A and plane B be line C, make a straight line D perpendicular to C on plane A and a straight line E perpendicular to C on plane B. If line D is perpendicular to line E, plane A is perpendicular to plane B..
6. Plane parallelism: Let straight lines a 1 and a2 be two intersecting straight lines in plane A, and b 1 and b2 are two intersecting straight lines in plane B. If A1/b1and a2//b2, plane A is parallel to plane B.
Vector method:
1. Straight lines are perpendicular: the direction vectors of two straight lines are perpendicular to each other.
2. Line-plane verticality: the direction vector of a straight line is parallel to the normal vector of the plane.
3. Parallel lines: The direction vectors of two straight lines are parallel to each other.
4. Line-plane parallelism: the direction vector of the straight line is perpendicular to the normal vector of the plane.
5. Faces are vertical: the normal vectors of two planes are perpendicular to each other.
6. Parallel planes: the normal vectors of two planes are perpendicular to each other.
After the coordinate system is established, the coordinates of each point can be obtained, and it is easy to get the direction vector of the straight line. The cross product of the direction vector of two intersecting straight lines on a plane can be taken as the normal vector of the plane.