How do you add two zero vector ? Is there any meaning in it ? $\vec{0}+\vec{0}$ =?

Question

Is there anything interesting from math point of view when adding two zero length vectors ? Do you get same vector that points in all directions same way ?

$\vec{0}+\vec{0}$ =?

Answer 1

think about what zero vector is: a vector without length, so zero vector plus zero vector is like this: $$\begin{pmatrix} 0\\ 0\\ \vdots\\ 0\\ \vdots\\ 0 \end{pmatrix}+ \begin{pmatrix} 0\\ 0\\ \vdots\\ 0\\ \vdots\\ 0 \end{pmatrix}=\begin{pmatrix} 0+0\\ 0+0\\ \vdots\\ 0+0\\ \vdots\\ 0+0 \end{pmatrix}= \vec{0}$$

Answer 2

No. It's just like adding zero and zero.

Answer 3

The zero vector is a vector, so you can add the zero vector to it and get the same vector out, just like you can with any other vector.