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ERIC Number: EJ875473
Record Type: Journal
Publication Date: 2004
Pages: 5
Abstractor: As Provided
ISSN: ISSN-0740-8404
Equivalent Vectors
Levine, Robert
AMATYC Review, v26 n1 p12-16 Fall 2004
The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The author reasoned that if this were true, there should be a way to alter the B vector in such a way that the result of the cross-product is still unchanged, but was told that this was impossible. When the course ended and there was time to think about it again, the author went to work trying to solve the impossible, and quickly succeeded. At the same time, an interesting fact was discovered about the cross-product that allowed for success. The proof was not so quick and easy though, but eventually it was accomplished as well. The proof involves an interesting twist where I present the finale, although still unproven, along with several related equations. The flow of proven equations then skips over that unproven group and eventually proves one of the equations in the group, which in turn proves the entire group.
American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Postsecondary Education; Two Year Colleges
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A