# Write the projection of the vector $$\hat i - \hat j$$ on the vector $$\hat i + \hat j$$

Toolbox:
• Projection of $\overrightarrow a\: on \: \overrightarrow b$ is $\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b |}$
Step 1:
Let $\overrightarrow a=\hat i-\hat j$ and $\overrightarrow b=\hat i+\hat j$.
Projection of $\overrightarrow a\: on \: \overrightarrow b$ is given by $\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b |}$
$\overrightarrow a.\overrightarrow b=(\hat i-\hat j).(\hat i+\hat j)$
$\qquad\;=1-1=0$
$\mid \overrightarrow b\mid=\sqrt{1^2+1^2}$
$\mid \overrightarrow b\mid=\sqrt{2}$
Step 2:
Projection of $\overrightarrow a$ on $\overrightarrow b$ is $\large\frac{0}{\sqrt{2}}$
Projection of $\overrightarrow a$ on $\overrightarrow b$ is 0.