vector properties: addition, subtraction, scalar multiplcation, zero vector
vector components, resolving a vector into components
vector between 2 points, distance between 2 points
magnitude, length
unit vector
dot product: geometric and algebraic definitions, interpretation and
properties
cross product: geometric and algebraic definitions, interpretation and
properties
normal vector, orthogonality
direction angles and direction cosines
scalar and vector projections
applications:
angle between 2 vectors, perpendicularity, normal vectors, work,
vector problems dealing with velocity and direction of heading, tension
problems, equation
of a plane, area of a rectangle or triangle, volume of a parallelepiped
Lines and Planes and Surfaces
3d coordinate systems
equation of a sphere
distance: between 2 points, a point and a plane
equations of a line: vector, parametric, symmetric equations
equations of a plane: vector, scalar, linear equations
surfaces on page 808
be able to investigate, interpret, identify, plot and visualize/sketch
functions of several variables (including linear functions)
applications: determine if lines intersect or are parallel,
determine if 2 planes interesect or are parallel, determine the point of
interestion of 2 lines, determine the line of intersection of 2 planes,
distance from a point to a plane, angle of intersection between 2 planes
Review Homework for Chapter 12, pg 813: #1, 3-7, 10-13, 15-36; for #22, use formula from 12.4 #43; for #27 use formula from 12.5 #73
