Mathematics 1229A/B Lecture Notes - Lecture 3: Parallelogram, Dot Product, Cross Product

• School: Western University
• Department: Mathematics
• Course: Mathematics 1229A/B
• Professor: Kuzmin

Document Summary

Math 1229 lecture 3 dot & cross products. If u = (a1,a2) and v = (b1,b2) then u v = (a1,b1) + (a2,b2) Similarly, if u = (a1,a2,a3) and v = (b1,b2,b3) then u v = (a1,b1) + (a2,b2) + (a3+b3) Note: u v is always a scalar not a vector! Find u v where u = (3,5,0) and v = (4,-2,1) Let u, v, and w be vectors in r2 similar properties in r3. Then: u v = v u commutative, u (v+w) = u v + u w distributive, u (av) = (au) v = a(u v) a represents all scalars, u u = ||u||2 or ||u|| = (cid:1795) (cid:1795) Definition: the angle between two vectors u and v where u and v have the same initial point is the angle between these vectors such that 0o o 180o. Theorem: let o be the angle between vectors u and v, then u v = ||u|| ||v||coso.