Chapter 4
Vectors in Three Dimensions
The scalar (dot) product, the vector (cross) product, and lines and planes in 3D expressed with vectors.
Chapter progress — 0/8 concepts0%
4.1 Vectors in 3D and Their Components
4.2 The Scalar (Dot) Product
4.3 The Vector (Cross) Product
4.4 Lines in 3D Using Vectors
4.5 Planes in 3D Using Vectors
Try it yourself
🔬 Vector Addition
Best on a larger screenBuild 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 ↗