Question

Write the projection of the vector $\hat{i}-\hat{j}$ on the vector $\hat{i}+\hat{j}.$

Answer 1

$$\begin{gathered} \text{The projection of}\overrightarrow{a}\text{on}\overrightarrow{b}\text{is} \\ \left(\frac{\overrightarrow{a}.\overrightarrow{b}}{\left|\overrightarrow{b}\right|}\right) \\ \text{The projection of}\hat{i}-\hat{j}\text{on}\hat{i}+\hat{j}\text{is} \\ \frac{\left(\hat{i}-\hat{j}\right).\left(\hat{i}+\hat{j}\right)}{\left|\hat{i}+\hat{j}\right|} \\ =\frac{1-1}{\sqrt{1+1}} \\ =0 \end{gathered}$$