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wdlang
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it seems that the vector product between vectors in three dimensions is peculiar property of the three dimensional space
wdlang said:it seems that the vector product between vectors in three dimensions is peculiar property of the three dimensional space
The vector product, also known as the cross product, is a mathematical operation between two vectors in three-dimensional space that results in a third vector that is perpendicular to the original two vectors.
The vector product can be generalised to higher dimensions by using the concept of the exterior product, which involves multiplying two vectors in a higher dimensional space to create a new vector that is perpendicular to both of them.
The generalisation of the vector product to higher dimensions allows for the application of vector algebra and geometry in spaces with more than three dimensions, which is useful in various fields such as physics, engineering, and computer graphics.
Yes, the vector product can be generalised to any number of dimensions. However, it is most commonly used in three dimensions, and the generalisation to higher dimensions can become increasingly complex and less intuitive.
One limitation of generalising the vector product to higher dimensions is that it can only be applied to vectors in Euclidean spaces, which have a fixed number of dimensions and satisfy certain geometric properties. It cannot be extended to other types of spaces, such as curved spaces in differential geometry.