Is a point "P" on a plane considered a zero vector, PP, or is there a difference between a single point and a zero vector?
Can there be a polar representation of a single point? If so, would it be <0> ?
Interesting . . . "Zero" always raises strange questions.
There is always a difference between a point and a vector.Is a point on a plane considered a zero vector,
or is there a difference between a single point and a zero vector?
The point might be and the zero vector is: .
If you referring to the pole (origin), the polar coordinates are: .Can there be a polar representation of a single point?
If so, would it be ?
. . where the 'magnitude' is 0 and can be any angle.
Other points have coordinates such as: .
It would be quite fair if someone argued that yours is a philosophical rather than a mathematical question.
Vectors are hybrid objects in that a vector has both length and direction.
Here is a quotation from Melvin Hausner, a geometer at NYU, “The vector will be designated by 0 (read: zero, or the zero vector, depending on how fussy you are.) Thus is a way of writing .”
To answer your other question: .