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 ( \(- p \mathbf { i } + 2 p \mathbf { k }\) ) relative to \(O\), where \(p\) is a constant.
Given that vector \(\overrightarrow { P A }\) is perpendicular to \(l\),
- find the value of \(p\).
Given also that \(B\) is a point on \(l\) such that \(\angle B P A = 45 ^ { \circ }\),
- find the coordinates of the two possible positions of \(B\).