If $\overrightarrow{A}=2\hat{i}+3\hat{j}-\hat{k}$  and $\overrightarrow{B}=-\hat{i}+3\hat{j}+4\hat{k}$ , then projection of $\overrightarrow{A}$  on $\overrightarrow{B}$  will be:

$\left|\overrightarrow{A}\right|=\sqrt{2^2+3^2+{\left(-1\right)}^2}=\sqrt{4+9+1}=\sqrt{14}$ 

$\left|\overrightarrow{B}\right|=\sqrt{{\left(-1\right)}^2+3^2+4^2}=\sqrt{1+9+16}=\sqrt{26}$

$\overrightarrow{A}\cdot \overrightarrow{B}=2\left(-1\right)+3\times 3+\left(-1\right)\left(4\right)$$=3$

The projection of $\overrightarrow{A}$  on $\overrightarrow{B}$

$=\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{\left|\overrightarrow{B}\right|}=\frac{3}{\sqrt{26}}$