Wonderful! You just take the two vectors and add them component-by-component. $$\vec{A} = 5\hat{i} - 3\hat{j}$$ and $$\vec{B} = 12\hat{i} + 7\hat{j}$$
So, for the x-component, you take the $$5$$ from $$\vec{A}$$ and the $$12$$ from $$\vec{B}$$ and add them together to get $$17$$. Similarly, for the y-component, you take the $$-3$$ and the $$7$$ and add them together to get $$4$$
If $$\vec{A} = 3\hat{i} - 4\hat{j}$$, $$\vec{B} = 10\hat{i} + 2\hat{j}$$ and $$\vec{C} = 8\hat{i} - 10\hat{j}$$, what is $$\vec{A} + \vec{B} + \vec{C}$$?
• $$21\hat{i} - 12\hat{j}$$
• $$12\hat{i} - 21\hat{j}$$
• $$-21\hat{i} - 12\hat{j}$$
• $$12\hat{i} + 21\hat{j}$$