Two particles $A$ and $B$ start moving from the origin in the $xy$-plane. Particle $A$ moves with a velocity of $20 \, m/s$ along the $x$-axis,and particle $B$ moves with a velocity of $30\sqrt{2} \, m/s$ at an angle of $45^{\circ}$ with the $x$-axis. The relative velocity of $B$ with respect to $A$ is ........... $m/s$.

• A
  $(10 \hat{i} + 30 \hat{j})$
• B
  $(30 \hat{i} + 10 \hat{j})$
• C
  $(30 \hat{i} - 20\sqrt{2} \hat{j})$
• D
  $(30\sqrt{2} \hat{i} + 10\sqrt{2} \hat{j})$