**Learning objectives**

- Work with algebraic and geometric linear combinations of vectors
- Work with dot product algebraically and geometrically
- Compute projections of vectors
- Connect vectors and planes in 3-space

**Before class**

- Read Hughes-Hallett sections 13.1-3.
- Ponder Hughes-Hallett problems: 13.1: 1, 5, 12, 26, 30, 38; 13.2: 1, 3, 5, 6, 22; 13.3: 1, 7, 11, 15, 32, 33, 35, 38, (70 for a theoretical challenge).

**In class**

- A few comments about vectors
- Equations of planes
- Activity: vector calculations
- Mathematica for vectors

**On your own**

- The cross product and torque
- Read On Contour and Slope Lines (1859) by Arthur Cayley