MindMap Gallery Solid Geometry Class Notes
This is a mind map of solid geometry class notes. The notes include the basic theorem of space vectors, inferences, operations, definitions, unit vectors and zero vectors, etc.
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Solid Geometry-Line and Plane Position Relationship Theorem
solid geometry
Sorting out knowledge points Geometry
2021/8/11 Class Record
definition
In space, there is direction and size (directed line segments)
mold
The size (length) of the vector
|a|≥0
Parallel vectors (collinear vectors)
Two vectors with the same or opposite directions
The baselines of two vectors are parallel or coincident
Vector b = λ vector a
unit vector
In space, a vector with modulus length 1
In space, the starting points of all unit vectors coincide with each other, and the end points form a sphere with a radius of one.
zero vector
|0|=0
Any direction
Rule: Parallel to any vector
Operation
addition
Subtraction
Multiply numbers
quantity product
a*b=|a||b|cos<a,b>
Change base
coordinate
a²=a*a=|a||a|cos0=|a|²
|a|=√a²
Square first and then take the square root
a⊥b←→a*b=0
inference
ABC three points collinear
AB=xAC
OA=xOB yOC and x y=1
ABCD four points are coplanar
AB=xAC yAD
OA=xOB+yOC zOD and x y z=1
Fundamental Theorem of Space Vectors
a//b←→a=xb
The three vectors abc are coplanar ←→a=xb yc
Three non-coplanar vectors abc in space can represent any vector in space
op=xa yb zc
direction vector
λ is the baseline of vector AB
Vector AB is the λ direction vector