1. The problem asks to find the vector $\vec{AB}$ given points $A(-2,6)$ and $B(8,-5)$.\n\n2. The formula for vector $\vec{AB}$ is $\vec{AB} = (x_B - x_A)\hat{i} + (y_B - y_A)\hat{j}$.\n\n3. Substitute the coordinates: $x_B = 8$, $x_A = -2$, $y_B = -5$, $y_A = 6$.\n\n4. Calculate the components:\n$$\vec{AB} = (8 - (-2))\hat{i} + (-5 - 6)\hat{j} = (8 + 2)\hat{i} + (-11)\hat{j} = 10\hat{i} - 11\hat{j}.$$\n\n5. Therefore, the vector $\vec{AB} = 10\hat{i} - 11\hat{j}$.\n\n6. The correct answer is option a. $\boxed{\vec{AB} = 10\hat{i} - 11\hat{j}}$.