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

uxuyvxvy