The method for testing the surface verticality is as follows:
1. If a straight line in one plane is perpendicular to the other plane, it can be said that the two planes are perpendicular. It can also be understood that if the straight line m is perpendicular to a plane, then any plane passing through the straight line m is perpendicular to this plane.
2. If the perpendicular of one plane is parallel to the other plane, the two planes are perpendicular.
3. If the normal vectors of two planes are perpendicular to each other, then the two planes are perpendicular. This method needs to establish a spatial rectangular coordinate system, express point coordinates, and find the normal vector of each plane before it can be proved. It can also be translated into that if the perpendicular lines of two planes are perpendicular to each other, then the two planes are also perpendicular.
The vertical theorem of a straight line is as follows:
1. If a straight line is perpendicular to a plane, then it is perpendicular to all straight lines in the plane.
2. Through a point in space, there is one and only one straight line perpendicular to the known plane.
3. If one of two parallel straight lines is perpendicular to a plane, then the other straight line is also perpendicular to this plane.
Two straight lines perpendicular to the same plane are parallel.
5. If a straight line is perpendicular to two intersecting straight lines on the plane, then this straight line is perpendicular to the plane.
Vector vertical introduction:
In mathematics, vectors (also known as Euclidean vectors, geometric vectors and vectors) refer to quantities with magnitude and direction. It can be imagined as a line segment with an arrow. The arrow indicates the direction of the vector; Line segment length: indicates the size of the vector. Only the magnitude corresponds to the vector, and the quantity without direction is called quantity (called scalar in physics).
Vector symbols are printed as bold letters (such as A, B, U, V), and a small arrow "→" is added at the top of the letters when writing. If the starting point (a) and the ending point (b) of the vector are given, the vector can be recorded as AB (and added to the top →). In the spatial cartesian coordinate system, vectors can also be expressed in pairs. For example, (2,3) in the Oxy plane is a vector.
In physics and engineering, geometric vectors are more often called vectors. Many physical quantities are vectors, such as the displacement of an object, the force exerted on it by a ball hitting a wall and so on. On the contrary, it is scalar, that is, a quantity with only size and no direction. Some definitions related to vectors are also closely related to physical concepts. For example, vector potential corresponds to potential energy in physics.