Answer
The vectors are perpendicular.
Work Step by Step
Recall the dot product property for n-dimensional vectors, which states that if $\vec{u}=(u_1,u_2.....u_n)$ and $\vec{v}=(v_1,v_2.....v_n)$, then their dot product is:
$\vec{u}\cdot \vec{v}=u_1v_1+u_2v_2+........u_nv_n$
$[(b \cdot c) a -(a \cdot c) b ] \cdot \vec{c} =(b \cdot c) a \dot c -(a \cdot c ) b \cdot c \\=(b \cdot c) (a \cdot c)-(b \cdot c) (a \cdot c)\\=0$
This shows that the dot product is $0$, so the vectors are perpendicular.
