Vectors
Vectors are the bridge between algebra, geometry, and physics. They show up anywhere direction matters, from motion and forces to 2D/3D coordinate systems and transformation problems. This learning path starts with visual intuition, then moves into hands-on manipulation and a deeper lab for vector thinking. Finish with a compact reference so you can quickly recall the formulas and notation you’ll use most often.
Learning Path
Vector Components and Resolution
See how magnitude and direction split into x- and y-components using trig, the core idea behind most vector problems.
Open →Vector Operations Visualizer
Add, subtract, and compare vectors interactively to build intuition for direction, resultant vectors, and component form.
Open →Parametric, Polar & Vector Lab
Connect vectors to parametric motion and polar ideas while experimenting with coordinates, direction, and movement.
Open →Vectors & Vector Operations
A quick refresher for notation, operations, and the most common vector formulas.
- Magnitude, direction, and component form are the essential building blocks.
- Use trigonometry to resolve vectors into x/y parts and reconstruct them from components.
- Review addition, subtraction, scalar multiplication, and common vector notation.
More Resources
Tools
Labs
Worksheets
Cheat Sheets
Infographics
Explainers
Common Questions
What is the main idea behind a vector?
A vector represents both size and direction. In math, that usually means an arrow or an ordered pair/triple that can be broken into components.
Why do vectors use trigonometry?
Trig lets you convert between a vector’s magnitude-direction form and its component form, which makes calculations much easier in geometry and physics.