# Show: Vectors e.g.(a,b,1) do not form vector space.

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1. Aug 12, 2018

### Pushoam

1. The problem statement, all variables and given/known data

2. Relevant equations
definition of null vector,

3. The attempt at a solution
null vector : $|0 \rangle = (0,0,0)$
inverse of (a,b,c) = ( - a, -b, -c)
vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same form. So, the vectors of the form ( a,b,1) do not form a vector space.

Is this correct?

Last edited: Aug 12, 2018
2. Aug 12, 2018

### Staff: Mentor

Yes, or even easier $(0,0,0) \notin \{\,(a,b,1)\,\}$.

3. Aug 12, 2018

### Pushoam

Thanks for it.