- Applications
- Suppose you’re an insect flying in such a manner that in 1 second your
position changes by ⟨ 4, 1, 5 ⟩ (feet). What’s your speed?
- Force and pushing furniture
- Suppose you’re an insect flying in such a manner that in 1 second your
position changes by ⟨ 4, 1, 5 ⟩ (feet). What’s your speed?
- Theory
- Prove property 8 on page 700 (distributive property)
- i.e., a(u+v) = au + av
- i.e., a(u+v) = au + av
- Show that magnitude does not distribute over addition
- i.e., |u+v| ≠ |u| + |v|
- i.e., |u+v| ≠ |u| + |v|
- Can you have 4 dimensional vectors? 5? More?
- Yes
- Operations scale up
- Are there such things as 1-dimensional vectors? If so, what do vector
addition and scalar multiplication look like when applied to them?
- Exactly like those operations on other vectors, and very much like standard numeric operations
- i.e., vector operations are sensible generalizations of scalar operations
- Prove property 8 on page 700 (distributive property)
- Vectors in muPad
- Problem Set
- “Products” of vectors — dot product
- ⟨ x1, x2, x3 ⟩ ⋅ ⟨ y1, y2, y3 ⟩ = x1y1 + x2y2 + x3y3
- = |x| |y| cos a
- Read section 12.3