Standard +0.3 This is a standard perpendicular from origin to line problem requiring dot product of OP with direction vector equals zero, then solving for λ. It's slightly easier than average as it's a routine textbook exercise with clear methodology and straightforward algebra, though it does require understanding of perpendicularity conditions in 3D.
6
\end{array} \right) + \lambda \left( \begin{array} { r }
2
- 3
1
\end{array} \right) \text { where } \lambda \text { is a scalar parameter. }$$
The point \(P\) lies on \(l _ { 1 }\). Given that \(\overrightarrow { O P }\) is perpendicular to \(l _ { 1 }\), calculate the coordinates of \(P\).\\
(ii) Relative to a fixed origin \(O\), the line \(l _ { 2 }\) is given by the equation
$$l _ { 2 } : \mathbf { r } = \left( \begin{array} { r }
4
- 3
6
\end{array} \right) + \lambda \left( \begin{array} { r }
2 \\
- 3 \\
1
\end{array} \right) \text { where } \lambda \text { is a scalar parameter. }$$
The point $P$ lies on $l _ { 1 }$. Given that $\overrightarrow { O P }$ is perpendicular to $l _ { 1 }$, calculate the coordinates of $P$.\\
(ii) Relative to a fixed origin $O$, the line $l _ { 2 }$ is given by the equation
$$l _ { 2 } : \mathbf { r } = \left( \begin{array} { r }
4 \\
- 3 \\
\hfill \mbox{\textit{SPS SPS FM Pure 2026 Q6 [10]}}