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## Q. 2.6

Let u = 2i 3j and v = i + j. Find $Proj_{v}$ u.

## Verified Solution

Here $(\mathbf{u} \cdot \mathbf{v}) /|\mathbf{v}|^{2}=-\frac{1}{2}, \text { so that } \operatorname{Proj}_{\mathbf{v}} \mathbf{u}=-\frac{1}{2} \mathbf{i}-\frac{1}{2} \mathbf{j}$. This is illustrated in Figure 6.