KeyConcepts
Key Concepts:
Vector arithmetic:
Vector arithmetic
Finding Angles:
Law of Cosines
Test for 90* between vectors (orthagonality
Dot product (used in calculation)
Given triangle sides find their angle
Combining Vectors:
Find 3rd triangle side given 2 sides
Find new vector (diagonal) from combining vectors
Given vector and angle, find length of vector at angle
Component (one vector projected onto another)
Areas:
Triangle area
Determinant: parallelogram area (two triangles)
Volume (3d area found with determinants)
Cross Product:
Cross product
Direction (i.e. direction of a vector in 3d)
Equations of Planes:
(i.e. find if point exists in a plane [flat region in a 3d space])
Matrix Multiplication:
Matrix Product (Multiplication)
Calculate matrix inverse. Use it with Ax = b (linear system) to transform one matrix into another
System of Equations:
Solving a system of equations
Intersection points as solutions to systems of equations
Equations of Planes:
Calculating normals
Find a vector that is the intersection between two planes
Find if a vector and a plane are parallel
Parametric Equations:
Representing and finding lines with parametric equations including x,y,z and t (time)
Finding intersections of lines with parametric equations
Line Intersecting with a Plane:
Find point of intersection of a line with a plane
Parametric Curves:
Graphing Circles, Eclipses, and Other Shapes
Cycloids and Measuring Distance Traveled on an Axis
Approximation of Point Near Bottom of Cycloid
Speed, Velocity, and Acceleration. Tangent Vectors
Arc Length, Velocity, Distance Traveled Along a Curve
Kepler's Second Law: Area is Swept Out by Line from Sun to Planet at a Constant Rate
Partial Derivatives:
Computing Partial Derivatives