Long description: block3fig1

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A graph shows a line segment drawn from the origin to the point (4, 5), labeled with the vector \(\mathbf{r} = 4\mathbf{i} + 5\mathbf{j}\).

Alt text: A graph shows a line segment drawn from the origin to the point (4, 5), labeled with the vector \(\mathbf{r} = 4\mathbf{i} + 5\mathbf{j}\).

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  • The image displays a two-dimensional coordinate system with a horizontal axis labeled \(x\) and a vertical axis labeled \(y\).
  • A straight line segment is drawn starting at the origin, denoted by \(O\), and terminating at the point \(P\) with coordinates (4, 5).
  • The line segment is associated with a vector notation, \(\mathbf{r} = 4\mathbf{i} + 5\mathbf{j}\), indicating the components of the vector in terms of the standard basis vectors \(\mathbf{i}\) and \(\mathbf{j}\).
  • An angle is indicated at the origin, formed between the vector \(\mathbf{r}\) and the positive \(x\)-axis.

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