The points \(A, B, C\) have position vectors
\(4 \mathbf{i}+5 \mathbf{j}+6 \mathbf{k}, \quad 5 \mathbf{i}+7 \mathbf{j}+8 \mathbf{k}, \quad 2 \mathbf{i}+6 \mathbf{j}+4 \mathbf{k},\)
respectively, relative to the origin \(O\). Find a cartesian equation of the plane \(A B C\).

The point \(D\) has position vector \(6 \mathbf{i}+3 \mathbf{j}+6 \mathbf{k}\). Find the coordinates of \(E\), the point of intersection of the line \(O D\) with the plane \(A B C\).

Find the acute angle between the line \(E D\) and the plane \(A B C\).