The angle between the straight lines $\overline{r}=\left(1-t\right)\left(4\overline{i}-\overline{j}\right)+t\left(2\overline{i}+j-3\overline{k}\right)$ and $\overline{r}=\overline{i}+2\overline{j}-\overline{k}+s\left(3\overline{i}-4\overline{k}\right)$ is

First line is passing through $A(4,-1,0),B(2,1,-3)$ with d.r.s $(2,-2,3)$ second line is passing through to $3\overline{i}-4\overline{k}$ with d.r.s  $(3,0,4)$

$\theta ={\cos }^{-1}\left(\frac{6+0+12}{\sqrt{17}\cdot \sqrt{25}}\right)={\cos }^{-1}\left(\frac{18}{5\sqrt{17}}\right)$