Let \(A(4,3,-2)\), \(B(0,-4,2)\), and \(C(-4,7,6)\) be the vertices of a triangle \(ABC\). If \(D(p,q,r)\) is the point of intersection of the bisector of angle \(A\) and the side \(BC\), then \(2p+q+r=\)
Show Hint
Whenever a point is formed by the intersection of an angle bisector and the opposite side of a triangle, immediately think of the Angle Bisector Theorem:
\[
\frac{BD}{DC}=\frac{AB}{AC}.
\]
After finding the ratio, use the section formula to obtain the coordinates.