L24 Math 233 Lecture Notes - Lecture 1: Equivalence Relation, Dot Product, J-Ax

• School: WUSTL
• Department: Mathematics
• Course: L24 Math 233
• Professor: Shapiro Jack

Document Summary

*all vectors are bolded unless specifically noted otherwise* Equivalence relation: 2 vectors are equal if same length and direction. Dot product: u: v |u||v|cos( ) = a1 b1+a2 b2+a3b3 u = < a1 ,a2 ,a3 > v = < b1 ,b2 ,b3 > u - v = < a1 b1 ,a2 b2 ,a3 b3 > |u - v 2 = |u 2 +|v 2. |u - v 2 = a3 b3 2 a2 b2 2+ a1 b1 2+ . Properties of dot products: a, scalar projection of b on a: a = |a 2 a) com pa(b) A = b cos( ) a b: vector projection of b on a: A : a pro ja(b) a b a) [a and b are vectors, i, a a j, and k are vector directions] Area of parallelogram: |a x b| = |a||b|sin( ) Non-zero orthogonal vector"s magnitude times 1/2 = area of a triangle. x=xo+at , y = yo+bt.