Standard +0.3 This is a straightforward application of the integrating factor method to a vector differential equation with constant coefficients. While the vector context adds slight novelty compared to scalar versions, the solution is mechanical: identify integrating factor e^(2t), multiply through, integrate, and apply initial conditions. The 6 marks reflect routine execution rather than conceptual challenge, making it slightly easier than average.
3. The position vector \(\mathbf { r }\) of a particle \(P\) at time \(t\) satisfies the vector differential equation
$$\frac { \mathrm { d } \mathbf { r } } { \mathrm {~d} t } + 2 \mathbf { r } = 4 \mathbf { i }$$
Given that the position vector of \(P\) at time \(t = 0\) is \(2 \mathbf { j }\), find the position vector of \(P\) at time \(t\).
(Total 6 marks)
3. The position vector $\mathbf { r }$ of a particle $P$ at time $t$ satisfies the vector differential equation
$$\frac { \mathrm { d } \mathbf { r } } { \mathrm {~d} t } + 2 \mathbf { r } = 4 \mathbf { i }$$
Given that the position vector of $P$ at time $t = 0$ is $2 \mathbf { j }$, find the position vector of $P$ at time $t$.\\
(Total 6 marks)\\
\hfill \mbox{\textit{Edexcel M5 2006 Q3 [6]}}