Find the scalar projection of $\vec{a}=\hat{i}+\hat{j}$ on $\vec{b}=\hat{i}-\hat{j}$.

Solution

1. The scalar projection of $\vec{a}$ on $\vec{b}$ is $\frac{\vec{a}\cdot \vec{b}}{|\vec{b}|}$.
2. Calculate the dot product: $$\begin{array}{rl}(1)(1)+(1)(-1)& =1-1\\ & =0\end{array}$$.
3. Since the dot product is zero, the projection is zero.
4. Hence the answer is (B).