OAB

Inputs
|A|
|B|
θ (angle A↔B)

Resultant
|R|
Direction

Addition of Vectors

Two vectors add up to a third one, and there are three different ways to find it. Here you get all of them side by side. The triangle law slides the second vector to the tip of the first. The parallelogram law completes a shape and takes the diagonal. The component method breaks everything into x and y first, then adds the numbers. All three give the same answer.

Controls

Four tabs across the top: Triangle Law, Parallelogram, Both, Component Method. In the first three, drag the tips of A and B to change them. In Component Method you step through four stages — Input vectors, Drop perpendiculars, Component arrows, Add them up — and you can add up to four vectors or drop back to two. Head to tail rearranges them into a chain.

Variables and outputs

Magnitudes of A and B, the angle between them, and the resultant with its direction. In Component Method, the x parts and y parts collect on their own axes and add up separately.

Model assumptions

Two dimensions only. No subtraction.

Learning objective

You should be able to find a resultant by any of the three methods and get the same answer each time.