1. **Stating the problem:** We have a vector of length 6 units that makes an angle of 30° with the y-axis. We need to find its coordinates. 2. **Formula and explanation:** The vector length (magnitude) is given by $|\vec{v}| = 6$. If the vector makes an angle $\theta = 30^\circ$ with the y-axis, then its components can be found using trigonometry: $$x = |\vec{v}| \sin \theta$$ $$y = |\vec{v}| \cos \theta$$ This is because the angle is with the y-axis, so the y-component is adjacent side and x-component is opposite side. 3. **Calculate components:** $$x = 6 \times \sin 30^\circ = 6 \times \frac{1}{2} = 3$$ $$y = 6 \times \cos 30^\circ = 6 \times \frac{\sqrt{3}}{2} = 3\sqrt{3}$$ 4. **Final coordinates:** $$\boxed{(3, 3\sqrt{3})}$$ 5. **Check options:** The coordinates match option (a) (3, 3√3).