Point \(A\) has coordinates \((-4,3)\) and point \(B\) has coordinates \((4,7)\).
Find the vector \(\overrightarrow{BA}\).[2]
Point \(C\) has coordinates \((x,7)\) and \(|\overrightarrow{AC}|=4\sqrt{10}\).
Find the two possible values of \(x\).[4]
Point \(D\) lies on the line \(AB\).
\(AD:DB=3:1\).
Find the equation of the line perpendicular to \(AB\) that passes through point \(D\).
Give your answer in the form \(y=mx+c\).[5]