The line $L$ has vector equation

(i) Find the position vector of the point $N$, the foot of perpendicular from the point $A$ with coordinates $(3,6,1)$ to the line $L$.

[3]

(ii) Find the position vector of the point $A^{\prime}$, the reflection of point $A$ in the line $L$.

[2]

(iii) Find the coordinates of the points on the line $L$ that are $3 \sqrt{3}$ units away from point $A$.

[2]