How do you divide a two or three component vector by another?
Or how do you take the same vector to the power of negative one?
I.E. :: V^(-1).
Thank you :).
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How do you divide a two or three component vector by another?
Or how do you take the same vector to the power of negative one?
I.E. :: V^(-1).
Thank you :).
As far as I know, there is no such thing as vector division. You can divide by the length of a vector, which just ends up being scalar multiplication. What's your application? Why would you need to divide a vector by another?
[EDIT]: See here.
Note that Ackbeet's link refers to vectors that can be represented by complex numbers and quaternions which are specifically vectors of dimension 2 and 4. In general there is NO definition for multiplying two vectors together and so no definition for powers of vectors or vector division.
It may be that in a specific application, one can define a "type" of division. Or perhaps you are confusing division by the length of a vector with division by the vector.
Well, aside from the dot product and the cross product. The result of a dot product is a scalar, so right there you're stuck if you want to do anything more. Technically, you could do vector cross product after vector cross product. But a vector crossed with itself is the zero vector, so powers of a vector defined in terms of the cross product would get kinda uninteresting pretty quick.Quote:
In general there is NO definition for multiplying two vectors together and so no definition for powers of vectors or vector division.
Cheers.
Yes, I completely forgot about the cross product. But that only applies to three dimensional vector spaces and, in any case, does not have an inverse. And I don't count the dot product- the result of a dot product is a scalar, not another vector, and so is not a "true" product.
Right-ho.
assuming inner product as the definition of vector multipication, by the standard definiton of division, c divided by a is b st
a.b=c
However, as pointed out by AckBeet, the dot product is a scalar, and since there is no general definition of vector product such that ab=c, vector division is meaningless.
I forget, is there a general n dimensional definition of vector cross product? If so, then you could define divison as above. For three dimensions and the standard definition of cross product, c divided by a is b st aXb=c. But that doesn't work either since bXa = -aXb. However, you could define division by one or the other, and then you would have to investigate whether there is a solution fo every c and a, a unequal to zero.