← Playground
03
Vector Playground
Two arrows on a plane. Drag either head and everything else follows — lengths, directions, the parallelogram of their sum, and the dot product that tells you how much they agree.
MODE
u=(3, 2)v=(-1, 3)
u + v=(2, 5)
Drag either arrowhead. The dashed copies show the head-to-tail construction: slide v to the tip of u and you land on u + v.
- u
- (3, 2)
- v
- (-1, 3)
- |u|
- 3.606
- |v|
- 3.162
- Direction of u
- 33.7°
- Direction of v
- 108.4°
- u + v
- (2, 5)
- u · v
- 3
- Angle between
- 74.7°
u · v = 3 — acute angle — the vectors broadly agree.
Positive means the angle is under 90°, zero means exactly 90°, negative means over 90°.
COORDINATES