Find the projection of a vector i + j on i + j.

\(\begin{aligned}\text{Projection}&=\frac{(\hat{i}+\hat{j})\cdot (\hat{i}+\hat{j})}{|\hat{i}+\hat{j}|}\\ &=\frac{2}{\sqrt{2}}\\ &=\sqrt{2}\end{aligned}\)