A car A moves along north with velocity 30 km/h and another car B moves along east with velocity 40 km/h. The relative velocity of A with respect to B is

Relative velocity of car A w.r.t. ground

 v_Ag = 30 km/h

Relative velocity of car B w.r.t. ground

v_Bg = 40 km/h

$\therefore$  Relative velocity of A w.r.t. B,  

      ${\mathbf{v}}_{AB}={\mathbf{v}}_{Ag}-{\mathbf{v}}_{Bg}={\mathbf{v}}_{Ag}+\left(-{\mathbf{v}}_{Bg}\right)$

     $\left|{\mathbf{v}}_{AB}\right|=\sqrt{(30{)}^2+(40{)}^2}=50 \mathrm{km}/\mathrm{h}$ 

$\therefore$              $\tan \theta =\frac{30}{40}=\frac{3}{4}$

$\Rightarrow$                  $\theta ={\tan }^{-1}(3/4)\mathrm{N}\text{ of west }$