Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

Cross Products and Tripple Vector Products in 3-dimensional Euclidian Space


Kanchun
Shinshu University, Nagano
Hiroshi Yamazaki
Shinshu University, Nagano
Yatsuka Nakamura
Shinshu University, Nagano

Summary.

First, we extend the basic theorems of 3-dimensional euclidian space, and then define the cross product in the same space and relative vector relations using the above definition.

MML Identifier: EUCLID_5

The terminology and notation used in this paper have been introduced in the following articles [14] [2] [12] [9] [5] [4] [3] [6] [13] [10] [11] [7] [8] [1]

Contents (PDF format)

Bibliography

[1] Kanchun   and Yatsuka Nakamura. The inner product of finite sequences and of points of $n$-dimensional topological space. Journal of Formalized Mathematics, 15, 2003.
[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[7] Czeslaw Bylinski. The sum and product of finite sequences of real numbers. Journal of Formalized Mathematics, 2, 1990.
[8] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[9] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[10] Jaroslaw Kotowicz. Real sequences and basic operations on them. Journal of Formalized Mathematics, 1, 1989.
[11] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[12] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[13] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[14] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

Received August 8, 2003


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