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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- September 3rd 2010, 08:31 AMjasper353Vector Division
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 :). - September 3rd 2010, 10:00 AMAckbeet
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. - September 3rd 2010, 10:06 AMHallsofIvy
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. - September 3rd 2010, 10:21 AMAckbeetQuote:

In general there is NO definition for multiplying two vectors together and so no definition for powers of vectors or vector division.

Cheers. - September 3rd 2010, 05:02 PMHallsofIvy
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.

- September 3rd 2010, 05:28 PMAckbeet
Right-ho.

- September 4th 2010, 07:56 AMHartlw
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.