Vectors · manipulative

The triangle rule

Drag a and b. Place b tip-to-tail after a to build the sum, or join their tips to build the difference — the resultant closes the triangle.

a b resultant

Drag a and b · scroll zoom · drag background to pan · Shift+drag an axis to dilate

Operation

Show parallelogram
the same sum, seen a second way (sum only)
Show resultant
reveal the vector that closes the triangle

The vectors

Working