1. space vector: the operation and properties of space vectors are the basis of solid geometry, but many students are confused about the concepts and formulas of vector addition, subtraction, scalar product and cross product.
2. The positional relationship between a straight line and a plane in space: it is an important problem in solid geometry to judge whether a straight line is parallel, perpendicular or intersecting with a plane, but it involves the calculation and judgment of the direction vector of a straight line and the normal vector of a plane, and many students are prone to make mistakes.
3. Spatial angle: The calculation and nature of spatial angle is an important content of solid geometry, but it involves the conversion and calculation of angle, which is easily confused by many students.
4. Volume and surface area of space geometry: To calculate the volume and surface area of space geometry, different formulas and methods need to be applied, such as the calculation formulas of triangular prism, cone and sphere, which are easily confused and memorized by many students.
5. Projection of spatial geometry: The projection of spatial geometry is to map the geometry in a certain direction to a plane, which involves the selection of projection lines and the determination of projection points. Many students are prone to make mistakes.
6. Symmetry of space geometry: Symmetry of space geometry includes rotational symmetry and mirror symmetry, which involves the selection of symmetry axis and the determination of symmetry plane, and many students are easily confused.
7. Cutting and combination of space geometry: Cutting a space geometry into multiple parts or combining multiple space geometries into a whole involves the judgment of section shape and position, and many students are prone to make mistakes.