“Cross Product”的概念、定义、习题解题方法及翻译-数学辞典

单词

Cross Product

释义

Cross Product

For Vectors and ,

(1)

This can be written in a shorthand Notation which takes the form of a Determinant

(2)

It is also true that

			(3)
			(4)

where

is the angle between

and

, given by the Dot Product

(5)

Identities involving the cross product include

(6)

(7)

(8)

(9)

For a proof that

is a Pseudovector, see Arfken (1985, pp. 22-23). In Tensornotation,

(10)

where

is the Levi-Civita Tensor.

See also Dot Product, Scalar Triple Product

References

Arfken, G. ``Vector or Cross Product.'' §1.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 18-26, 1985.

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