Physics & Mathematics · Interactive learning companion

Parallelogram Law of Vector Addition

Use the parallelogram construction to predict the resultant of two vectors of different magnitudes and directions.

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Parallelogram Law of Vector Addition

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📝 Description

Parallelogram Law of Vector Addition is an interactive simulation for visualizing the resultant of two vectors. Students change vector magnitudes and directions, observe the parallelogram construction, and connect graphical addition with vector reasoning.

📋 Instructions

Adjust the sliders and observe how the resultant changes. Compare the diagram, values, and vector construction to understand the parallelogram law.

🎓 Learning Guide: Parallelogram Law of Vector Addition

Learning focus: Use the parallelogram construction to predict the resultant of two vectors of different magnitudes and directions.

Physics & Mathematics Interactive learning companion

Learning objectives

Identify head-to-tail or parallelogram vector addition.
Relate resultant magnitude to the included angle between two vectors.

Concepts and principles

For magnitudes A and B with included angle θ, |A+B|=√(A²+B²+2AB cosθ).
Parallel vectors add magnitudes; perpendicular vectors combine through Pythagoras.

Examples and worked solutions

Find the resultant of perpendicular vectors of magnitudes 3 N and 4 N.: Worked solution: The magnitude is √(3²+4²)=5 N.

Try this activity

Observe the described vector magnitudes and direction sliders.
Predict a resultant for a simple 90° case before comparing with the on-screen parallelogram.