Chapter 2: Vectors Notes

Sections

1. 2A Introducing vectors Mastered

   Vectors as directed line segments, magnitude, equal, opposite, parallel and zero vectors, adding vectors head to tail and by the parallelogram rule, subtraction, and scalar multiples.

   Open notes
2. 2B Components of vectors Mastered

   The unit vectors i and j, components and column vector notation, magnitude and direction from components, unit vectors, operations with components, position vectors, and vectors between two points.

   Open notes
3. 2C The dot product Mastered

   The dot product or scalar product defined geometrically, the angle between two vectors, perpendicular vectors, the algebraic laws for the dot product, and using it to prove geometric results.

   Open notes
4. 2D Three-dimensional space Mastered

   Coordinates in three dimensions, right-handed axes, the coordinate planes, distances and midpoints in space, and the equation of a sphere.

   Open notes
5. 2E Vectors in three dimensions Mastered

   The unit vectors i, j and k, components and column vectors in three dimensions, magnitude, unit vectors, operations with components, position vectors, and parallel vectors and collinear points.

   Open notes
6. 2F The dot product with components Mastered

   The component formula for the dot product in two and three dimensions, its proof from the distributive law, finding angles between vectors, testing for perpendicular vectors, and finding unknown components.

   Open notes
7. 2G Projections Mastered

   The projection of one vector onto another, its length, the component of a vector perpendicular to another, resolving a vector into perpendicular parts, and the distance from a point to a line.

   Open notes