Vector Division: Is It Possible?

[neutrino]

From school, we've had addition, "subtraction" of vectors and then scalar multiplication, dot & cross products. I have never come across dividing a vector by another. Is there such an operation?

Eagerly awaiting enlightening replies,
Nanveeth

 

[matt grime]

In order to have division one needs a multiplication which for which the cancellation property holds (amongst other things)

xy=xz => y=z

what multiplication do you want to use? cross product won't do...

actually there is a way of defining a multiplication such that there is a division for two dimensional vectors (have you heard of complex numbers?).

 

[neutrino]

This is actually a general question that I have and I'm not planning to use it anywhere for now.

Btw, I'm a second-year physics undergrad.

 

[matt grime]

And my answer still remains: division is defined in terms of multiplication. 1/2 is the number which when multiplied by 2 yields 1 etc.

The complex numbers are a two dimensional real vector space which posses such a multiplication. THe quaternions a 4-d real vector space.

In *general* we do not have a division of vectors.

I don't know what being a second year physics undergrad means per se in relation to my post (was it supposed to indicate you know what complex numbers are? If you were at Cambridge then you'd know what complex numbers are, if you were at some less than stellar state or private university in the US then you probably wouldn't)