3. By the end of Week 2:
You would learn how to plot equations in 2 variables in 3-space and how to describe and manipulate with vectors.
These are just few examples:
find an orthogonal projection of a vector onto a given direction vector
represent a vector as the sum of two vectors, one being parallel to a given direction vector and the other being orthogonal
find a vector perpendicular to two given vectors
find the volume of the a parallelepiped with adjacent sided being given vectors

5. The Dot Product:
Properties of the Dot Product:

6. The Dot Product Formula:

7. Direction Angles; Direction Cosines
direction cosines of v:

8. Exercises:

9. Vector and scalar components along standard unit vectors:
2-space
Vector components
Scalar components
3-space

10. The orthogonal projection on a unit vector:
Vector components are the orthogonal projections on standard unit vectors:

11. The orthogonal projections on an arbitrary nonzero vector b:
is the projection on the unit vector in the direction of v
The vector component orthogonal to b:

12. Solving work problems:

14. Proofs involving the dot product:

15. The cross product of two vectors in 3-space
*The determinant is a mnemonic device only!

16. Properties of the cross product

17. Geometric properties of the cross product
Using the right-hand rule to determine the direction of u x v

18. Exercises:

19. Exercises:

20. The scalar triple product
Geometric properties of the scalar triple product

21. Algebraic properties of the scalar triple product

22. Exercises:

23. Exercises: