MindMap Gallery Vector algebra and spatial analytic geometry
The figure below summarizes the understanding, analysis and idea map of vector algebra and space analytic geometry.
Edited at 2020-09-20 12:45:47This 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.
Chapter 7 Vector Algebra and Space Analytic Geometry
vector
concept
definition
Has size and direction
mold
unit vector
collinear vector
coplanar vector
direction angle
direction cosine
nature
Operation
addition
Number multiplication vector
Note: Multiplying a vector by 0 results in a vector of 0, not the number 0
Quantitative product of vectors
formula
Vector operations
Coordinate operations
Meaning: The result is a number
application
Find the module length
Find the angle between two vectors (extended to find the angle between two straight lines, a straight line and a plane, and two planes)
Determine vertical
Expanded to prove the perpendicularity of two straight lines, two planes, and the parallelism of a straight line and a plane
Find the distance from a point to a plane
Create a plane point French equation
vector product of vectors
formula
Vector operations
Coordinate operations
Meaning: The result is a vector perpendicular to both a1 and a2
application
Find the area of the parallelogram (a and b are adjacent sides)
distance from point to straight line
Judgment of parallelism
Mixed product
express
Coordinate operations
Meaning: The result is a number
application
Three vectors are coplanar
Calculation of common vertical line
Establish plane equations
algorithm
Addition and multiplication
quantity product
vector product
The difference is: the result of the quantity product swap remains unchanged, but the vector product needs to add a negative sign after the swap.
Mixed product
Plane and straight line
flat
plane equation
Point French equation
form
Meaning: (A, B, C) is a normal vector
general equation
Form Ax By Cz D=0
Vector
parametric
The idea of determining the plane
method one
Given the points on the plane and the normal vector of the plane, use the point normal equation to get
Method Two
Given a point on the plane and two non-collinear vectors on the plane, the equation of the plane can be determined
Extension method two
Given a point on the plane and two non-collinear vectors on the plane, then assuming x, the vector from x to the point is coplanar with the other two vectors, so the mixed product is 0. Establish an equation
straight line
Equation of a straight line
General form (interface form)
parametric
Symmetry formula [(l,m,n) is the direction vector]
The idea of determining the equation of a straight line
method one
A point on a straight line and the direction vector of the straight line
Method Two
Two non-parallel planes intersect in a straight line
projection of space curve
Solution ideas
First establish the parametric equation, and then enter the plane equation later to solve the parameter value and obtain the projection.
Equations and representations of common surfaces of revolution, cylinders, and quadratic surfaces
Relationship between straight lines and planes and distance formulas
relationship between two planes
parallel judgment
vertical judgment
Calculation of included angle (not greater than 90 degrees)
relationship between two straight lines
parallel judgment
vertical judgment
Calculation of included angle (not greater than 90 degrees)
Relationship between straight lines and planes
parallel judgment
vertical judgment
Calculation of included angle (90 degrees minus calculated angle)
plane beam equation
Distance formulas between points, straight lines, and planes
Note that the angle Θ refers to the angle that does not exceed π