In what direction should the airplane fly not to miss the airport? Here is the question:
A plane sights an airport at $[N30°E]$ and is travelling at a speed of 500km/hr. There is a wind from $[N30°W]$ at a speed of 25km/hr. Determine the reading the airplane must travel in order not to miss the airport.
Options are:
a) $[S18°W]$
b) $[N45°E]$
c) $[S14°W]$
d) $[N18°E]$
Here is how I approached the problem, although my answer doesn't match up with any answer provided. Maybe someone can spot my error?
Assume the airplane resides at the origin. Let $\vec{v}=\Big<500\cos(\theta),500\sin(\theta)\Big>$ denote the velocity of the airplane, where $\theta$ is an angle to be determined. We can represent the velocity of the wind by $$\vec{u}=\Bigg<25\cos(-\pi/3),25\sin(-\pi/3)\Bigg>=\Bigg<\frac{25}{2},-\frac{25\sqrt3}{2}\Bigg>$$
To answer this question, we need to find the angle $\theta$ which makes the resultant vector $\vec{v}+\vec{u}$ point in the direction of the airport, which is $$\Bigg<\cos(\pi/3),\sin(\pi/3)\Bigg>=\Bigg<\frac{1}{2},\frac{\sqrt3}{2}\Bigg>$$
In other words, we need to solve the equation for $\theta$. $$\frac{\vec{v}+\vec{u}}{||\vec{v}+\vec{u}||}=\Bigg<\frac{1}{2},\frac{\sqrt3}{2}\Bigg>$$
This yields $\theta \approx 1.091$ which  is equivalent to $N27.5^{\circ} E$. Can anyone help me figure out what I'm doing wrong? Thank you.

I would leave a comment but I do not have the reputation to do so.
I believe your problem is with the wind vector.
The wind is coming from $N30°W$, which means it is blowing in a direction $S60°E$. This would make both components of the wind vector negative.
