8. With respect to a fixed origin \(O\), the line \(l\) has equation $$\mathbf { r } = \left( \begin{array} { c } 13
8
1 \end{array} \right) + \lambda \left( \begin{array} { r } 2
2
- 1 \end{array} \right) \text {, where } \lambda \text { is a scalar parameter. }$$ The point \(A\) lies on \(l\) and has coordinates \(( 3 , - 2,6 )\).
The point \(P\) has position vector ( \(- \boldsymbol { i } + 2 \boldsymbol { k }\) ) relative to \(O\).
Given that vector \(\overrightarrow { P A }\) is perpendicular to \(l\), and that point \(B\) is a point on \(l\) such that \(\angle B P A = 45 ^ { \circ }\), find the coordinates of the two possible positions of \(B\).
(5)
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