Vector Equation: Can I Divide Vectors?

[hotcommodity]

If I have z= ||v||u + ||u||v, can I say that (z/uv) = (||v||/v) + (||u||/u) ? I'm not sure if I can divide vectors that way...

 

[Moo Of Doom]

It's meaningless to divide something by a vector. In general, that operation is not defined. What you could do in this case, though, is divide by the norms of the vectors instead. That yields some useful information:

$$\frac{z}{||u||||v||}=\frac{u}{||u||}+\frac{v}{||v||}$$

 

[hotcommodity]

It's meaningless to divide something by a vector. In general, that operation is not defined. What you could do in this case, though, is divide by the norms of the vectors instead. That yields some useful information:

$$\frac{z}{||u||||v||}=\frac{u}{||u||}+\frac{v}{||v||}$$

Haha, I just wrote something similar in my notebook but it didn't register with me. Thank you