The component of $\overrightarrow{a}=2\widehat{i}+3\widehat{j}$  along the direction of vectors $(\widehat{i}+\widehat{j})$ and  $(\widehat{i}-\widehat{j})$ respectively are  

$\overline{a}=2\overline{i}+3\overline{j}$

$\overline{b}=\overline{i}+\overline{j}$                                 

Component of ‘a’ along ‘b’, $\text{a}\cos \theta =\frac{2\left(1\right)+3\left(1\right)}{\sqrt{2}}$

$a\cos \theta =\frac{a.b}{\left|b\right|}=\frac{2+3}{\sqrt{2}}=\frac{5}{\sqrt{2}}$

Component of $\overrightarrow{a}$

$\text{along\hspace{0.17em}c\hspace{0.17em}}\Rightarrow \text{\hspace{0.17em}a}\cos \theta =\frac{\text{a.c}}{\left|c\right|}=\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.$