What quantity did you change?
Labs / Mathematics
Vector Playground
Grab the colored tip of either vector and drag it anywhere. The gray arrow traces their sum by the parallelogram rule, the shaded bar shows how much of a lies along b, and the readouts track the dot product and the angle between them.
Labs / Mathematics / Vector Playground
Vector Playground
Grab the colored tip of either vector and drag it anywhere. The gray arrow traces their sum by the parallelogram rule, the shaded bar shows how much of a lies along b, and the readouts track the dot product and the angle between them.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
a (3.0, 0.0) |3.00|b (0.0, 3.0) |3.00|R (3.0, 3.0) |4.24|a·b 0.00θ 90°
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Line the two vectors up so they point the same way. What does the angle read, and what happens to the dot product?
- Make the vectors perpendicular. Why does the dot product collapse to zero exactly then?
- Swing one vector past 90° so the two oppose each other. When does the dot product turn negative?
- Switch from sum to difference. Where does a − b point compared to a + b?
- Press “Normalize both”. The arrows shrink to length 1 — does the angle between them change at all?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.