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Perfect! For \(\vec{A} - \vec{B}\), you need to subtract the x- and the y-components separately. The x-component will be \(8-10\) and the y-component will be \(4-2\).
If \(\vec{A} = 3\hat{i} - 4\hat{j}\), this is the same as writing

\(\vec{A} = 3\hat{i} + \left(-4\right)\hat{j}\) That is, the y-component of \(\vec{A}\) is \(-4\). If

\(\vec{B} = -5\hat{i} - 6\hat{j}\)

\(\vec{A} - \vec{B} = \left(3 - \left(-5\right) \right) \hat{i} + \left(-4 - \left( -6 \right) \right) \hat{j}\) \(= 8 \hat{i} + 2 \hat{j}\)
If \(\vec{A} = -2\hat{i} - 5\hat{j}\) and \(\vec{B} = -8\hat{i} + 3\hat{j}\), what is \(\vec{A} - \vec{B}\)?
  • \(-10\hat{i} + 2\hat{j}\)
  • \(6\hat{i} - 8\hat{j}\)
  • \(-6\hat{i} - 2\hat{j}\)
  • \(6\hat{i} + 2\hat{j}\)