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Wonderful! The method is simple. You must just add the x- and y-components of \(\vec{A}\) and \(\vec{B}\) and subtract those of \(\vec{C}\) from this sum. So, the x-component will be \(5+3-2\) and the y-component will be \(4+7-12\).
We have talked about addition and subtraction. What about multiplication? We will consider the multiplication of two vectors later. For now, let's look at multiplying a vector by a number. This is called scalar multiplication. If

\(\vec{A} = A_x \hat{i} + A_y \hat{j}\),

\(3 \vec{A} = 3 A_x \hat{i} + 3 A_y \hat{j}\)

That is, you just multiply each component by the number.
If \(\vec{A} = 3 \hat{i} - 2 \hat{j}\), what is \(5 \vec{A}\)?
  • \(15 \hat{i} + 10 \hat{j}\)
  • \(10 \hat{i} + 15 \hat{j}\)
  • \(15 \hat{i} - 10 \hat{j}\)
  • \(10 \hat{i} - 15 \hat{j}\)