Let u = 2i + 3j and v = i + j. Calculate Projv u.

Question

Let u = 2i + 3j and v = i + j. Calculate [latex]Proj_{v}[/latex] u.

Accepted Answer

[latex]\operatorname{Proj}_{\mathbf{v}} \mathbf{u}=(\mathbf{u} \cdot \mathbf{v}) \mathbf{v} /|\mathbf{v}|^{2}=\left[5 /(\sqrt{2})^{2}\right] \mathbf{v}=(5 / 2) \mathrm{i}+(5 / 2) \mathbf{j}[/latex]. This is illustrated in Figure 5.

Question 2.5: Let u = 2i + 3j and v = i + j. Calculate Projv u.

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