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Chapter 9

Introduction to Vectors

Geometric vectors and the Triangle Law, using vectors to prove classic geometry results, position vectors, and two-dimensional (column) vector notation.

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9.1 Geometric Vectors

Scalar and Vector QuantitiesEasy
Representing and Naming VectorsEasy
Adding and Subtracting Vectors GeometricallyMedium

9.2 Applications to Elementary Geometry

Using Vectors to Prove Geometric ResultsHard
Ratio and Division of a Line Segment Using VectorsHard

9.3 Position Vectors

Position Vectors and the OriginMedium
Finding a Vector Between Two PointsMedium

9.4 Two-Dimensional Vectors

Column Vector Notation and ComponentsMedium
Magnitude of a Two-Dimensional VectorMedium

Try it yourself

🔬 Vector Addition

Best on a larger screen

Build vectors on a grid, change their length and angle, and add them together to see the resultant.

Try this: Drag vectors onto the grid from the tray, then drag their tips to change magnitude and direction.

Look for: Turn on "Sum" and see how the resultant vector is the same whichever order you add the vectors in.

Simulation by PhET Interactive Simulations, University of Colorado Boulder — licensed CC BY-NC. View on phet.colorado.edu ↗

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