MATH 1920 Lecture Notes - Lecture 3: Cross Product, Dot Product, Determinant

• School: Cornell University
• Department: Mathematics
• Course: MATH 1920
• Professor: Andrew Sale

Document Summary

Proof of the formula for the cross product using the definition of the dot product (not required for quizzes/exams): u = v = Let n = such that u n = 0 and v n = 0. By definition of the dot product: (1) u1n1 + u2n2 + u3n3 = 0 (2) v1n1 + v2n2 + v3n3 = 0. Take: n1 = v3u2 - u3v2 n2 = v3u1 - u3v1. By (1): n3 = u1v2 - u2v1 n = is one of infinitely many vectors orthogonal to u and v. Definition: the cross product of u and v is: u x v = 2. u x v is orthogonal to both u and v. ||u x v || = ||u|| ||v|| sin for 0 < <= . ||u x v|| = 0 u x v = 0.