I think what this post means is the following.
Is this correct?
Thanks for the reply. That was not what I am driving at.
I think:
1) should still be
2) should be equal to 1!!!!
This is because a unit vector is a unit vector whether the magnitude of the original vector is zero or some function.
I just want to see what other people think.
Hello, yungman!
I think your questions are asking for undefined quantities.
If , the vector has length 0; it is a point,
. . It has no direction.
The unit vector does not exist.
Now you are asking for the magnitude of a unit vector that does not exist.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Having said that, I did a "mind experiment."
We have a vector: .
Its unit vector is:.
And you claim that: .
That is, that all vectors (however small) have a unit vector of length 1.
I must admit that your claim has merit . . .