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