1. Establish an appropriate rectangular coordinate system.

2. Let the plane normal vector n=(x, y, z).

3. Find two vectors that are not * * * straight lines in the plane, and record them as a=(a 1, a2, a3) b=(b 1, b2, b3).

4. According to the definition of normal vector, the equation 1NA = 02NB = 0 is established.

5. Solve the equation and take one of the solutions. ?

Based on:

① Because there are countless straight lines perpendicular to the known plane in space, there are countless normal vectors (including two unit normal vectors) in a plane.

(2) If a straight line is perpendicular to two intersecting straight lines in the plane, then this straight line is perpendicular to the plane.

Extended data:

The normal vector of 1. plane is an important vector to determine the position of the plane, and it refers to a non-zero vector perpendicular to the plane. A plane can have an infinite number of normal vectors, but there are only two unit normal vectors.

For example, in the space rectangular coordinate system, the normal vector of plane Ax+By+Cz+D=0 is n=(A, b, c), and its unit normal vector, that is, the normal vector divided by the length of the normal vector, indicates the direction.

Second, for a triangle-like polygon, the cross product of two non-parallel sides of the polygon is the normal of the polygon.

3. the plane represented by the equation ax+by+cz=d, and the vector (a, b, c) is its normal.

4. If the surface has no tangent plane at a certain point, then there is no normal at that point. For example, the vertex and bottom edge of a cone have no normals, but the normals of the cone exist almost everywhere. Usually, a surface that satisfies Lipschitz continuity can be considered that normals exist almost everywhere.

Five, the general usage of undetermined coefficient method:

Let all or part of the coefficients of a polynomial be unknown, and determine these coefficients by using the principle that the coefficients of two polynomial identities are equal or other known conditions, so as to get the value to be found. For example, if a known polynomial is decomposed into factors, the coefficients of some factors can be set as unknowns, and these unknowns can be obtained by using the conditions of identities.

References:

Baidu Encyclopedia-Normal Vector

Baidu encyclopedia-vertical line and plane