Law of Vector Addition

Triangle Law • Parallelogram Law • Polygon Law

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Vector Values

Resultant R: Magnitude: 0.00 Direction: 0.0°

What is a Vector?

A vector is a quantity that has both magnitude (size) and direction. Examples include displacement, velocity, force, and acceleration. Vectors are represented as arrows — the length shows magnitude, the arrowhead shows direction.

Triangle Law

Place two vectors head-to-tail. The resultant vector R joins the tail of the first vector (A) to the head of the last vector (B). Mathematically: R = A + B.

R = A + B

How to Use

Drag the arrowheads on the canvas to adjust vectors visually

• Use sliders below the canvas for precise values

• Switch between Triangle, Parallelogram, and Polygon tabs

• In Polygon mode, add or remove vectors with the buttons

• Watch the resultant update in real-time

Key Points

• The Triangle Law and Parallelogram Law give the same resultant for the same two vectors — they are just different visual methods

• The Polygon Law generalizes vector addition to any number of vectors

• Vector addition is commutative: A + B = B + A

• Vector addition is associative: (A + B) + C = A + (B + C)