Proving the sum of the 2 vectors

Question

"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 $(a1+a2,b1+b2)$.

Answer 1

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

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

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

$= (a_1, b_1)$

Similarly,

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

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

$= (a_2, b_2)$

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

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

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