MATH 32A Lecture Notes - Lecture 3: Vector Projection, Distributive Property, 5,6,7,8

• School: UCLA
• Department: Mathematics
• Course: MATH 32A
• Professor: Austin, A.D.

Document Summary

Definition: given two vectors v = and w = , their dot product (or inner product/scalar product) is v (dot) w = a 1 a 2 + b 1 b 2 + c 1 c 2 . Thus, the result of a dot product of two vectors is a scalar, not a vector. Many people make this mistake, so be careful. It"s a 1 a 2 + b 1 b 2 + c 1 c 2 , not . <1,3> (dot) <2,5> = 1(2) + 3(5) = 2 +15 = 17. Example: <2, 1, 3> (dot) <4, -2, -5> = 2(4) + 1(-2) + 3(-5) = 8 - 2- 15 = -9. Algebraic properties of dot products: 0 (dot) v = 0. V (dot) w = w (dot) v.