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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 \(4\)
Adding three vectors is very similar to adding two vectors. You just include the x- and the y-components of the third vector too.
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 \(\vec{A} + \vec{B} + \vec{C}\)?
  • \(21\hat{i} - 12\hat{j}\)
  • \(12\hat{i} - 21\hat{j}\)
  • \(-21\hat{i} - 12\hat{j}\)
  • \(12\hat{i} + 21\hat{j}\)