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

## Homework Equations

definition of null vector,
[/B]

## 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?

#### Attachments

• upload_2018-8-12_19-29-5.png
23.5 KB · Views: 649
• upload_2018-8-12_19-40-16.png
4.3 KB · Views: 568
Last edited:

## Answers and Replies

fresh_42
Mentor
2021 Award
Yes, or even easier ##(0,0,0) \notin \{\,(a,b,1)\,\}##.

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

Thanks for it.