Question

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

Answer 1

The correct answer is: 0
Let $\vec{a}=\hat{i}-\hat{j}$ and $\vec{b}=\hat{i}+\hat{j}$
Now,projection of $\vec{a}$ on $\vec{b}$ is given by,
$\frac{1}{|\vec{b}|}(\vec{a}.\vec{b})=\frac{1}{\sqrt{1+1}}[1.1+(-1)(1)]=\frac{1}{\sqrt{2}}(1-1)=0$
Hence,the projection of vector $\vec{a}$ and $\vec{b}$ is 0.