Vectors - Notes and Question Bank

Basic Stuff

• INDEX
• Some general rules
• Adding vectors and what this can mean physically
• Using components to describe vectors
• Basic trig for working out components
• Trying to pull a boulder up a hill
• Finding the magnitude or length of a vector

Multiplying vectors

• The scalar or dot product and work done by a force
• Finding the direction cosines of a vector
• The vector or cross product and the moment of a force
• Can we multiply 3 vectors together? The vector triple product
• The scalar triple product and what it means geometrically

Lines and planes

• Finding the vector equation of a line
  
• Finding vector equations of planes
• Finding equations of planes using normal vectors
• Finding a normal vector
• Angles between lines and planes
• Equations of planes in the form Ax + By + Cz = D
• What does the equation 3x + 4y = 12 give us?
• Writing the equation of a line in 3 dimensions
• Examples of problems involving lines and planes

Extra bits

• Finding the shortest distance from a point to a line
• Finding the shortest distance between 2 skew lines
• Finding where the medians of a triangle intersect
• changing x,y,z coordinates into spherical polar coordinates
• Where next? (includes external links)

Copyright © Jenny Olive 1999 - 2003 (Last altered September 2003)