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Precisely! Scalar multiplication is very simple. We just have to multiply the x- and the y-components (\(3\) and \(-2\) respectively) by \(5\), that's it!
If \(\vec{A} = \hat{i} - \hat{j}\), \(\vec{B} = - 2 \hat{i} + 3 \hat{j}\) and \(\vec{C} = 2 \hat{i} + \hat{j}\), what is \(3 \vec{A} - 2 \vec{B} + 4 \vec{C}\)?
  • \(15 \hat{i} - 5 \hat{j}\)
  • \(9 \hat{i} + 7 \hat{j}\)
  • \(-9 \hat{i} - 7 \hat{j}\)
  • \(12 \hat{i} - 5 \hat{j}\)