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Resolve the vector represented by the directed line segment from (-2, 3) to (1, 5) into its vertical and horizontal components.
Using (7),
\mathbf{v}=\left(a_{2}-a_{1}\right) \mathbf{i}+\left(b_{2}-b_{1}\right) \mathbf{j}we have
\mathbf{v}=\left(a_{2}-a_{1}\right) \mathbf{i}+\left(b_{2}-b_{1}\right) \mathbf{j}=[1-(-2)] \mathbf{i}+(5-3) \mathbf{j}=3 \mathbf{i}+2 \mathbf{j}.