Vector Lab
Explore vector components, direction and operations in two and three dimensions.
Explore the lab
What you can explore
- Components and magnitude
Edit x, y and z components to see the arrow direction and calculated length change.
- Vector operations
Choose addition, subtraction, dot product or cross product and inspect the corresponding result.
- 2D versus 3D
Switch views and show component guides to connect coordinates with spatial direction.
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The model
Formula and underlying model
|A| = √(Ax² + Ay² + Az²); A + B = (Ax + Bx, Ay + By, Az + Bz)- A, B
- Input vectors (abstract vector units)
- Ax, Ay, Az
- Components of A along each axis (same units as A)
- |A|
- Magnitude or length of A (same units as A)
The 2D view uses x/y components; the 3D view includes z. A zero vector has no defined direction.
The experiment
How it works
Define vectors
Enter components for A and, when needed, enable B.
Choose an operation
Select a calculation and display its result vector or scalar.
Connect arrows to numbers
Use components and magnitude guides to interpret the result.
Learning outcomes
What you’ll learn
- Calculate magnitude from components.
- Explain cancellation of opposing vectors.
- Distinguish scalar results from vector results.
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Explore lab →Ready to experiment?
Explore Vector interactively
Open the lab, adjust the parameters, and see the results change in real time.