# Course Content

## Chapter 1: Euclidean n-space

#### Friday October 3 (slides)

§1.5, Linear Independence.

#### Wednesday October 1 (slides)

§1.4: Projections, and how we can use projections to find the distance from a point to a plane.

#### Monday September 29 (slides)

§1.4: Projections. This worksheet illustrates the projection of vectors in 3D.

#### Friday September 26 (slides)

We explore two parametric lines, and ask whether they intersect.

Regarding the line of intersection of planes, this Plane intersection worksheet will help with visualizations.

Still regarding the line of intersection of planes, this this video may be helpful.

Regarding the distance from a point to a plane, this video concerns similar ideas, and may be helpful.

#### Wednesday September 24 (slides)

More equations of lines. Again, try this Equation of line interactive graphic, and also this Two Parametric Lines one.

#### Monday September 22 (slides)

More cross product. Equation of a line in three-space. Try this Equation of line interactive graphic, and this Cross product of two vectors interactive.

#### Friday September 19 (slides)

More planes. Planes through three points.

#### Wednesday September 17 (slides)

Start §1.3. Visualizing planes. Equations of planes and normal vectors. Try this 3D Planes interactive graphic.

#### Monday September 15 (slides)

Dot product and angle between vectors. Finish §1.2 (omitted Cauchy-Schwartz inequality).

#### Friday September 12 (slides)

Linear combinations. Try this Linear combination interactive graphic. 3D coordinates and coordinate planes. Standard basis vectors. Finish §1.1 and begin § 1.2. Length and unit vectors.

#### Wednesday September 10 (slides)

Recap. Vector subtraction. Higher dimensions. Try this Vector Subtraction and scalar multiplication interactive graphic.

#### Monday September 8 (slides)

Scalar multiplication and addition. Try this Vector Addition and scalar multiplication interactive graphic.

#### Friday September 5 (slides)

Introduction. §1.1: Vectors and arrows. Vector between two points. Remember to return your flashcards at the end of term.

### Resources

Projection of vectors in 3D interactive.

Two parametric lines interactive.

Plane intersection visualization.

Cross product of two vectors interactive.