Answer
The vectors are perpendicular.
Work Step by Step
We are given that $\vec{a}=\sqrt 3 i+j$, $\vec{b}=3i+\sqrt 3 j$ and $c=i-\sqrt 3j$
$b=\sqrt 3 (\sqrt 3i+j)=\sqrt 3 a$
This implies that $b$ is a scalar product of $a$, and $a$& $b$ are parallel vectors.
Now, $a \cdot c=(\sqrt 3 i+j) \cdot (i-\sqrt 3 j)=0$
The dot product of the two vectors is $0$. This implies that a and c are also parallel to each other.
