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Magnitude of a Vector
Discover how to calculate the magnitude of a vector in 2D and 3D using a simple Pythagorean-based formula, with clear worked examples.
What You'll Learn
Identify the magnitude of a vector as its length, always a non-negative number
Apply the formula magnitude equals square root of x squared plus y squared for a 2D vector
Extend the formula to three dimensions by adding a z squared term under the square root
Calculate the magnitude of a vector joining two points by first subtracting coordinates
Recognize that dividing a vector by its own magnitude produces a unit vector
Connect magnitude to real situations such as combining forces into a resultant force
What You'll Practice
1
Finding magnitude from vectors plotted on coordinate grids
2
Calculating magnitude from component, rectangular, and matrix forms
3
Determining magnitude using initial and terminal point coordinates
4
Working with vectors parallel to axes (zero x or y components)
Why This Matters
Finding vector magnitude is essential in physics, engineering, and advanced math. You'll use this skill to calculate distances, forces, velocities, and in multivariable calculus. Understanding magnitude helps you analyze motion, optimize paths, and solve real-world navigation problems.
Before You Start — Make Sure You Can:
This Unit Includes
8 Video lessons
Practice exercises
Learning resources
Skills
Vectors
Magnitude
Pythagorean Theorem
Components
Distance Formula
Coordinate Geometry
OH Curriculum Aligned