Vectors & parametric curves

MATH 151 (Galveston, Spring 2026) places Appendix J before limits on the syllabus PDF. Stewart sections 1.5 (inverse trig) are on the schedule but there is no WebAssign PDF in materials/ for 1.5 yet.

Learning goals

• Represent vectors in $\mathbb{R}^2$ and $\mathbb{R}^3$; add, scale, and interpret geometrically.
• Use the dot product for projections, orthogonality, and work-as-force-through-distance templates.
• Write vector functions $\mathbf{r}(t)$ and connect to parametric curves $(x(t),y(t))$.

Concept sheet

A vector $\mathbf{v} = \langle v_1, v_2, v_3 \rangle$ has magnitude $\|\mathbf{v}\| = \sqrt{v_1^2+v_2^2+v_3^2}$. Dot product: $\mathbf{u}\cdot\mathbf{v} = \|\mathbf{u}\|\|\mathbf{v}\|\cos\theta$.

Parametric curve: $x=f(t)$, $y=g(t)$. Velocity vector $\langle x'(t), y'(t) \rangle$ points along the motion (derivative material returns in Appendix K later in the term).

Practice

Original drills — use Check when available, then Show solution. A quick celebration plays on correct auto-checks (respects reduced motion).

Homework / practice (WebAssign exports)

Section	Link	Notes
Appendix J.1 — Vectors	Open PDF	Week 1–2 on syllabus
Appendix J.2 — Dot product	Open PDF	After MLK week in official calendar
J.3 — Vector functions & parametric curves	Open PDF	Filename uses J.3 prefix

Mistakes & checks

• Dot product output is a scalar; cross product (if you meet it later) is a vector.
• When differentiating vector functions later, differentiate componentwise.

Quiz mode

Homework PDF quiz: each card links to the same WebAssign export filenames as the semester map (materials/). A session shows 20 shuffled cards from 45 PDF-linked slots; exact problem wording stays in the PDF unless you merge transcripts per quiz/transcripts/README.md. Regenerate: python3 scripts/gen_hw_quiz.py.