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"I need to prove summing 2 vectors, I'm given 3 points
1)$O(0,0)$
2)$A(a_1,b_1)$
3)$B(a_2, b_2)$
and that $a_1,a_2,b_1,b_2 > 0$. Using the Geometric Definition I need to define that the cordinates for the sum of the vectors $\vec{OA}$ and $\vec{OB}$ are $(a1+a2,b1+b2)$.

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    which are what? i will fix – 2017-01-28
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    2 things unclear from your question: 1) is $(a_1, a_2, b_1, b_2)$ a point? 2) Do you want to prove that $(a_1+a_2, b_1+b_2)$ is the sum of vectors $OA$ and $OB$? – 2017-01-28
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    Yes , and i fixed the problem – 2017-01-28

1 Answers 1

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$\vec{OA} = \vec{A} - \vec{O}$

$= (a_1, b_1) - (0,0)$

$= (a_1 - 0, b_1 - 0)$

$= (a_1, b_1)$

Similarly,

$\vec{OB} = \vec{B} - \vec{O}$

$= (a_2, b_2) - (0,0)$

$= (a_2, b_2)$

$\vec{AB} = \vec{OA} + \vec{OB}$

$= (a_1, b_1) + (a_2, b_2)$

$= (a_1 + a_2 , b_1 + b_2)$

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    is this the geometric definition that proves it? – 2017-01-28
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    Yes it is. Also see this http://www.suitcaseofdreams.net/Geometric_addition.htm – 2017-01-28