Question

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

Answer 1

Let $\overrightarrow{a}=\hat{i}-\hat{j}$ and $\overrightarrow{b}=\hat{i}+\hat{j}$.
Now, projection of vector $\overrightarrow{a}$ and $\overrightarrow{b}$ is given by,
$\frac{1}{|\overrightarrow{b}|}(\overrightarrow{a}\cdot \overrightarrow{b})=\frac{1}{\sqrt{1+1}}\{1.1+(-1\left)\right(1\left)\right\}=\frac{1}{\sqrt{2}}(1-1)=0$
Hence, the projection of vector $\overrightarrow{a}$ on $\overrightarrow{b}$ is $0$.