Ask for help How to learn dihedral angles, how to find dihedral angles

Did you choose science? If you are in liberal arts, you don't have to take a dihedral test.

It seems that (the point) first makes a perpendicular line perpendicular to the intersecting line, and then finds a projection in another plane to connect the vertical foot with the photography.

The normal vector can not be used only by the feet, and the angle of the normal vector is equal to the size of the dihedral angle.

As long as you can establish a spatial Cartesian coordinate system, and then find the normal vector of two planes, the angle between the normal vector is the magnitude of the dihedral angle, but it should be noted that it is also possible that the complementary angle is the size of the dihedral angle.

Normal vector that look for the second high school book B version of the book to take a look.

It's really good, but it has to be at right angles to use it.

The main thing is to find the dihedral.

It is recommended that you use the Dragon Gate Thematic Book Series.

109 Proving the parallel way of thinking of straight lines and straight lines.

1) Convert to determine that there is no intersection point of two coplanar straight lines;

2) Convert into two straight lines and parallel to the third straight line;

3) Convert to line and surface parallelism;

4) Convert to line and surface vertical;

5) Transform into face-to-face parallelism.

110 Ways of thinking that prove the parallel of straight lines and planes.

1) Convert to a straight line and plane without common points;

2) Convert to lines parallel to each other;

3) Transform into face-to-face parallelism.

111 Proving the way of thinking that the plane is parallel to the plane.

1) Convert to determine that there is no common point in the second plane;

2) Convert to line-surface parallelism;

3) Convert to line surface vertical.

112 Proving the perpendicular way of thinking of straight lines and straight lines.

1) Convert to intersecting perpendicular;

2) Convert to line-surface vertical;

3) translating into a line perpendicular to the projection of another line;

4) The converted line is perpendicular to the oblique line that forms the projection.

113 Proving that a straight line is perpendicular to a plane.

1) Convert the line to be perpendicular to any straight line in the plane;

2) the transformation of the straight line into two straight lines intersecting in the plane perpendicular to it;

3) the straight line is parallel to one of the perpendicular lines of the plane;

4) convert the line to perpendicular to another parallel plane;

5) Convert the line to be perpendicular to the intersection of two perpendicular planes.

114 Ways of thinking that prove the perpendicular plane to the plane.

1) Translate into judging that the dihedral angle is a straight dihedral angle;

2) Convert to line-surface vertical;

115.The law of addition of space vectors and the operation of number multiplication vectors.

1) Commutative law of addition: a b = b a

2) Associative property of addition: (a b) c = a (b c) 3) Number multiplication distributive property: (a b) = a b 116Generalization of the parallelogram rule of plane vector addition to space.

The sum of three vectors with the same start point and not in the same plane is equal to the vector represented by the diagonal line of a parallelepiped with a common start point in a parallelepiped with these three vectors as the edges.

The tips for finding the dihedral angle are as follows:1. The perpendicular method is the angle composed of the plane perpendicular to the edge, and the line that intersects the vertical plane and the dihedral angle, that is, the dihedral angle and the plane angle.

2. Definition method - take a point arbitrarily on the edge of the line, and make a perpendicular line of point A on the edge in both planes.

Sometimes the perpendicular line can be made perpendicular in two different planes, and then parallel to one of the perpendicular feet and the perpendicular line.

It is also possible to find the dihedral angle.

Common methods: The first is the definition method, just do it according to the definition, and if it is not common, it will be early.

The second is the angle finding method of the three-perpendicular line theorem, which is also the most common. For example, if you find the dilateral terror angle A-CD-B, then pass A to make the perpendicular line of the BCD plane, and the perpendicular foot is E, and then to make the perpendicular line of Cd through E, and the perpendicular foot is F, and connect Fa, then the angle AFE is the plane angle of the dihedral angle to be found.

The third bell is area photography. If the area of the triangle abc in face 1 is S1 and the def area of the projective triangle in 1 is S2, then the cosine of the dihedral angle of 1,2 is S2 S1

Finally, after knowing the method, you should do more questions and accumulate experience in order to achieve specific analysis of specific topics, so that you can be handy when doing questions.

The tips for finding the dihedral angle are as follows:

1. The vertical plane of the sedan chair - the angle composed of the plane perpendicular to the edge, and the line that intersects the vertical plane and the dihedral angle, that is, the dihedral angle and the plane angle.

2. Definition method - take a point arbitrarily on the edge, and make the perpendicular line of the land point A on the edge in both planes, sometimes the perpendicular line can be made in two different planes, and then guess the parallel line between the vertical foot and the perpendicular line in one of them, and you can also find the dihedral angle.

First find the intersection line of the two planes, and then find the straight line perpendicular to the intersection of the first roller line in the two planes, usually these two planes are special figures, such as: isosceles triangle only front, equilateral triangle. The intersection is the midpoint.

To find the dihedral angle, you can use the perpendicular method, the definition method, and the area projection theorem.

1. Vertical surface method.

If it is a plane perpendicular to the edge, the angle formed by the intersection of the two faces of the vertical plane and the dihedral angle is the plane angle of the dihedral angle. Let the intersection line of the dihedral angle be L1, and the dihedral angle and the perpendicular plane intersect the straight lines L2 and L3 respectively. Since the two faces of the dihedral angle are perpendicular to the same plane, l1 is perpendicular to kkk.

Therefore, according to the definition of the angle between the dihedral angle, the angle between L2 and L3 is the angle between the dihedral angle.

2. Definitions.

Take a point A on the edge, and then make a perpendicular line through point A on the edge in the two planes. Sometimes it is also possible to make perpendicular lines in two planes, and then pass one of the perpendicular feet to make a parallel line of the other perpendicular line. When using the definition method, you first need to convert it into a plane angle according to the definition of the dihedral angle, and then put this plane angle in a triangle, and find the dihedral angle by solving the triangle.

3. Area projection theorem.

The cosine of the dihedral angle is equal to the ratio of the area of the projection of one half plane in the other half plane to the area of the plane itself. i.e. the formula cos = s'/s。The key to using this method is to find the inclined polygon and the projection on the plane of the dihedral angle from the diagram, and the area of the angle of the dihedral angle is easy to find.

Dihedral:

A dihedral angle is a straight line in a plane that divides the plane into two parts, each of which is called a half-plane, and the figure composed of two half-planes starting from a straight line. The size of the dihedral angle can be measured by its plane angle, how many degrees is the plane loss angle of the dihedral angle, that is, how many degrees is this dihedral angle, and the dihedral angle of the plane angle is a right angle is called a straight dihedral angle.

Any two planar angles of the same dihedral angle are equal, and the larger dihedral angle has a larger planar angle. The plane angle corresponding to the sum or difference of the two dihedral angles is the sum or difference of the plane angles corresponding to the original two dihedral angles. Dihedral angles can be bisected, and bisected faces are unique.

The dihedral angles of the opposite edges are equal.

The magnitude of the planar angle of a dihedral angle is independent of the position of its vertices on the edge. If the two dihedral angles can coincide exactly, then the two dihedral angles are said to be equal. If the plane angles of the two dihedral angles are equal, then the two dihedral angles are equal.

Conversely, the plane angles of equal dihedral angles are equal to the pin angles.

The small vertical technique of finding the dihedral angle of the residual difference can be used to define the method, take a point A on the edge, and then make the perpendicular line of the point A on the edge in the two planes; Sometimes it is also possible to make perpendicular lines in two planes, and then pass one of the perpendicular feet to make a parallel line of the other perpendicular line. The figure composed of two half-planes from a straight line is called a dihedral angle, this straight line is called the edge of the dihedral angle, and these two half-planes are called the faces of the dihedral angle; The magnitude of the planar angle of a dihedral angle is independent of the position of its vertices on the edge.

Summary. Dihedral angle refers to the angle between two faces in three-dimensional space, and here are some points to pay attention to when solving dihedral angles:1

Determine the two faces: First, you need to identify the two faces that you want to solve the dihedral angle. These two faces can be planes, surfaces, or three-dimensional faces.

2.Select the normals of the two faces: The dihedral angle is determined by the normals of the two faces.

Therefore, before solving for the dihedral angle, it is necessary to explicitly choose which normal vector of which face. 3.Direction of the normal vector:

The direction of the normal vector is very important for calculating the dihedral angle. The direction of the normal vector is determined by taking into account the direction from one face to another. If the normal vector is in the wrong direction, the resulting dihedral angle will be a complement angle instead of the required dihedral angle.

4.Choosing a calculation method: There are different methods that can be used to calculate dihedral angles, including vector inner product, cosine theorem, etc.

The choice of the appropriate method for the calculation is based on the specific problem and the accuracy required. 5.System of Units:

When calculating dihedral angles, the same system of units should be used. If one face is represented in radians and the other is represented by angles, then a unit conversion is required when solving for dihedral angles. 6.

Accuracy issues: When making accurate calculations, there may be rounding errors or truncation errors. In order to get more accurate results, higher precision calculation tools or algorithms can be used.

Dihedral angle refers to the angle between two faces in three-dimensional space, and here are some points to pay attention to when solving dihedral angles:1Identify two faces:

First, you need to identify the two faces that you want to solve the dihedral angle. These two faces can be planes, surfaces, or three-dimensional faces. 2.

Select the normals of the two faces: The dihedral angle is determined by the normals of the two faces. Therefore, before solving for the dihedral angle, it is necessary to explicitly choose which normal vector of which face.

3.Direction of the normal vector: The direction of the normal vector is very important for calculating the dihedral angle.

The direction of the normal vector is determined by taking into account the direction from one face to another. If the direction of the normal vector is wrong, the resulting dihedral filial piety ridge will be a complementary angle instead of the required dihedral angle. 4.

Choosing a calculation method: There are different methods that can be used to calculate dihedral angles, including vector inner product, cosine theorem, etc. The choice of the appropriate method for the calculation is based on the specific problem and the accuracy required.

5.System of Units: The same system of units should be used when calculating dihedral angles.

If one face is represented in radians and the other is represented by angles, then a unit conversion is required when solving for dihedral angles. 6.Accuracy issues:

When making accurate calculations, there may be round-off errors or truncation errors. In order to get more accurate results, higher precision calculation tools or algorithms can be used.

The distance from a point to a polygon.