Question

Prove that the set of all three dimensional vectors forms a group under the operation addition.​

Answer 1

Every vector space is an abelian group under addition. It's an axiom

Proof:-

$V =\{ x = ( x_{1} ,x_{2} ,x_{3}) | x_{i}∈K\}$

$V\times V→V ,( x_{1} ,x_{2} ,x_{3})+( y_{1} ,y_{2} ,y_{3})=( x_{1} +y_{1},x_{2}+y_{2},x_{3}+y_{3})$