- Matlab/muPad
- Installers adjusted to provide muPad and other apps
- Re-download and re-install if muPad doesn’t work for you
- Section 12.2
- Components show how space is divided into dimensions
- Arithmetic rules and properties for vectors vs scalars
- Standard unit vectors i, j, k
- Notation: boldface for typed vectors, e.g., v vs v
- Arrow for hand-written vectors
- Arrow for hand-written vectors
- Length of vector v = ⟨ v1, v2, v3 ⟩ = |v| = √( v12 + v22 + v32 )
- Examples
- Ship sailing north at 15 mph launches dinghy sailing southwest
at √2 mph. What is dinghy velocity relative to ship?
- Gravity pulls a ball down with a force of 0.1 Newtons, while a
wind pushes the ball northwest with a force of 0.05 Newtons.
What is the net force?
- Express ⟨2,3⟩ as a⟨1,1⟩ + b⟨-1,1⟩
- This demonstrates a general truth, that any non-parallel set of n vectors can be used to describe points in n-dimensional space
- Ship sailing north at 15 mph launches dinghy sailing southwest
at √2 mph. What is dinghy velocity relative to ship?
- Vectors needn’t be restricted to 2 or 3 dimensions, they can have any dimensionality
- Problem Set
- The dot product
- Read section 12.3