6 The points \(P\) and \(Q\) have position vectors, relative to the origin \(O\), given by $$\overrightarrow { O P } = 7 \mathbf { i } + 7 \mathbf { j } - 5 \mathbf { k } \quad \text { and } \quad \overrightarrow { O Q } = - 5 \mathbf { i } + \mathbf { j } + \mathbf { k }$$ The mid-point of \(P Q\) is the point \(A\). The plane \(\Pi\) is perpendicular to the line \(P Q\) and passes through \(A\).

1. Find the equation of \(\Pi\), giving your answer in the form \(a x + b y + c z = d\).
2. The straight line through \(P\) parallel to the \(x\)-axis meets \(\Pi\) at the point \(B\). Find the distance \(A B\), correct to 3 significant figures.