Chapter 11

Working with vectors

1. Basic rules for handling vectors
   1. What are vectors?
   2. Adding vectors and what this can mean physically
   3. Using components to describe vectors
   4. Vector components in three-dimensional space
   5. Finding the magnitude of a three-dimensional vector
   6. Finding unit vectors

2. Multiplying vectors
   1. Defining the scalar or dot product of two vectors
   2. Working out the dot product of two vectors
   3. Defining the vector or cross product of two vectors
   4. Working out the cross product of two vectors
   5. Can we multiply three vectors together?
   6. The vector triple product
   7. The scalar triple product and what it means geometrically

3. Finding equations for lines and planes
   1. Finding a vector equation for a line
   2. Dealing with lines in two dimensions
   3. Dealing with lines in three dimensions
   4. Finding the cartesian equation of a line in three dimensions
   5. Another form for the vector equation of a line
   6. Finding vector equations for planes
   7. Finding equations of planes using normal vectors
   8. Finding the perpendicular distance from the origin to a plane
   9. The cartesian form of the equation of a plane
   10. Finding where a line intersects a plane
   11. Finding the line of intersection of two planes

4. Finding angles and distances involving lines and planes
   1. Finding the angle between two lines
   2. Finding the angle between two planes
   3. Finding the acute angle between a line and a plane
   4. Finding the shortest distance from a point to a line
   5. Finding the shortest distance from a point to a plane
   6. Finding the shortest distance between two skew lines

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