A man walks 4 mtrs. towards west and then walks 3 mtrs in the direction of $\large\frac{\pi}{6}\:$ radians east of north. What is the displacement of the man from the starting point?

Question

$\begin{array}{1 1} (A) -\large\frac{11}{4}\hat i+\large\frac{3\sqrt 3}{4}\hat j \\ (B) -\large\frac{11}{2}\hat i+\large\frac{3\sqrt 3}{2}\hat j \\ (C) -\large\frac{11}{2}\hat i+\large\frac{27}{4}\hat j \\ (D) -\large\frac{11}{4}\hat i+\large\frac{3}{2}\hat j\end{array}$