MindMap Gallery Spatial analytic geometry (without surfaces)
This is a mind map about spatial analytic geometry (without surfaces), including vector algebra, planes, straight lines, etc. I hope it will be helpful for you to learn mathematics!
Edited at 2023-11-12 19:33:16This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
Space Analytic Geometry
vector algebra
concept
The coordinates of the vector:
Modulus (size) of vector:
Unitization of vectors:
special vector
unit vector:
Zero vector:
Vector operations
Addition and Subtraction
addition
Coordinate expression:
Law of operation:
Subtraction:
Quantity product (dot product)
definition:
Coordinate expression:
nature:
The cosine formula of the angle between two vectors:
Satisfy/dissatisfy law
satisfy
distributive law
commutative law
dissatisfied
associative law
Vector product (cross product)
definition:
Coordinate expression:
nature:
Satisfy/dissatisfy law
satisfy
distributive law
dissatisfied
associative law
commutative law
Mixed product
definition:
Coordinate expression:
nature:
flat
plane equation
Point French:
General method:
Intercept type:
special plane equations
The constant term is 0:
A coefficient is 0
Both coefficients are 0
Relationship between two planes:
Necessary and sufficient conditions for mutual perpendicularity:
Necessary and sufficient conditions for mutual parallelism:
Necessary and sufficient conditions for mutual parallelism and overlap:
The formula for the angle between two planes:
Distance formula from point to plane:
straight line
Equation of a straight line
Symmetry equation:
Parametric equation:
General equation:
Angle between two straight lines
The relationship between two straight lines:
Necessary and sufficient conditions for two straight lines to be perpendicular:
Necessary and sufficient conditions for two straight lines to be parallel
straight lines and planes
Necessary and sufficient conditions for a straight line to be perpendicular to a plane:
Necessary and sufficient conditions for a straight line to be parallel to a plane
The angle between a straight line and a plane: