7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2ce10759-9ce6-47a1-b55d-d22082f88f55-16_330_654_246_751}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the straight line \(l\).
Line \(l\) passes through the points \(A\) and \(B\).
Relative to a fixed origin \(O\)
- the point \(A\) has position vector \(2 \mathbf { i } - 3 \mathbf { j } + 5 \mathbf { k }\)
- the point \(B\) has position vector \(5 \mathbf { i } + 6 \mathbf { j } + 8 \mathbf { k }\)
- Find \(\overrightarrow { A B }\)
Given that a point \(P\) lies on \(l\) such that
$$| \overrightarrow { A P } | = 2 | \overrightarrow { B P } |$$
find the possible position vectors of \(P\).