209

$\left|\overline{a}\right|=\sqrt{6^2+\left(-8\right)^2}=10$
$\overline{a}^0=\frac{\overline{a}}{\left|\overline{a}\right|}=\frac{6\overline{\text{i}}-8\overline{\text{j}}}{10}=\frac{3}{5}\overline{\text{i}}-\frac{4}{5}\overline{\text{j}}$
$\left|\overline{b}\right|=\sqrt{\left(-5\right)^2+12^2}=13$
$\overline{b}^0=\frac{\overline{b}}{\left|\overline{b}\right|}=\frac{-5\overline{\text{i}}+12\overline{\text{j}}}{13}=-\frac{5}{13}\overline{\text{i}}+\frac{12}{13}\overline{\text{j}}$

$\overline{AP}=5\overline{a}^0-26\overline{b}^0=3\overline{\text{i}}-5\overline{\text{j}}+10\overline{\text{i}}-24\overline{\text{j}}=13\overline{\text{i}}-29\overline{\text{j}}$
$\overline{OA}+\overline{AP}=-1\overline{\text{i}}+1\overline{\text{j}}+13\overline{\text{i}}-29\overline{\text{j}}=12\overline{\text{i}}-28\overline{\text{j}}$
$P=\left(12{,}\ -28\right)$