Chapter 8 Vector Algebra and Space Analytic Geometry

Knowledge logic structure diagram

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Postgraduate exam content

The concept of vector (free movement), linear operation of vectors, quantified product of vectors (is a number, commutative) and vector product (is a vector, change sign after exchange), mixed product of vectors (the nature of exchange is the same as that of the determinant , Geometric meaning, used to find the distance between straight lines on different planes), conditions for two vectors to be perpendicular (quantity product is zero), parallel (vector product and zero vector), and the angle between two vectors (surface, line, line) , Vector coordinate expression and operation, unit vector, direction angle and direction cosine, concept of surface equation and space curve equation, plane equation (point method, intercept, general, plane beam equation), straight line equation (symmetric Formula, parametric, general formula), plane and plane, plane and line, line and line parallel and perpendicular conditions (transformed into the relationship between vectors) point to plane and point to line distance (using parallelogram); Spherical surface, the generatrix is parallel to the cylindrical surface of the coordinate axis, the rotation axis is the equation of the rotating surface of the coordinate axis, the commonly used quadric surface equation and its graphics, the parameter equation and general equation of the space curve, the projection curve of the space curve on the coordinate surface equation.

Postgraduate exam requirements

1. Understand the space rectangular coordinate system, understand the concept of vector and its representation.
2. Master the calculation of vectors: linear operations, quantitative product (calculate the angle between vectors, determine perpendicularity), vector product (parallelogram area and the distance from a point to a straight line), mixed product (calculate the volume of a hexahedron and the length of the common vertical line of a different plane, determine Whether the three vectors are coplanar), understand the conditions for two vectors to be perpendicular and parallel.
3. Understand the coordinate expressions of unit vectors, direction angles, direction cosines, and vectors, and master the method of vector operations using coordinate expressions.
4. Master plane equations (point method, mixed product) and straight line equations (point method, general formula) and how to find them.
5. Will find the angle between plane and plane, plane and line, line and line, and use the relationship between plane and line (parallel, perpendicular, intersection, etc.) to solve related problems.
6. Will find the distance from the point to the straight line and the point to the plane.
7. Understand the concepts of surface equations and space curve equations.
8. Understand the equations and graphs of commonly used quadric surfaces, and be able to find the rotation surface with the coordinate axis as the rotation axis and the cylinder equation with the generatrix parallel to the coordinate axis.
9. Understand the parametric equations and general equations of space curves. Understand the projection of the space curve on the coordinate plane, and be able to find its equation.