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.
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°
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?