| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Linear combination of vectors |
| Difficulty | Easy -1.3 This is a straightforward vector addition question requiring only basic arithmetic with i and j components, followed by standard interpretation of the zero vector result in two physical contexts. The calculation is routine and the interpretations (equilibrium for forces, returning to start for displacement) are standard textbook applications with no problem-solving required. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement3.03a Force: vector nature and diagrams |
| Answer | Marks | Guidance |
|---|---|---|
| \(\mathbf{P} + \mathbf{Q} + \mathbf{R} = 0\mathbf{i} + 0\mathbf{j}\) | B1 [1] | Accept answer zero (condone it not being in vector form) |
| Answer | Marks | Guidance |
|---|---|---|
| The particle is in equilibrium | B1 | If "equilibrium" is seen give B1 and ignore whatever else is written. Allow "acceleration is zero", "the particle has constant velocity" and other equivalent statements. Do not allow "The forces are balanced", "The particle is stationary" as complete answers |
| Answer | Marks | Guidance |
|---|---|---|
| The hiker returns to her starting point | B1 [2] | Do not allow "The hiker's displacement is zero" |
## Question 2:
### Part (i)
$\mathbf{P} + \mathbf{Q} + \mathbf{R} = 0\mathbf{i} + 0\mathbf{j}$ | B1 [1] | Accept answer zero (condone it not being in vector form)
### Part (ii)(A)
The particle is in equilibrium | B1 | If "equilibrium" is seen give B1 and ignore whatever else is written. Allow "acceleration is zero", "the particle has constant velocity" and other equivalent statements. Do not allow "The forces are balanced", "The particle is stationary" as complete answers
### Part (ii)(B)
The hiker returns to her starting point | B1 [2] | Do not allow "The hiker's displacement is zero"
---2 The vectors $\mathbf { P } , \mathbf { Q }$ and $\mathbf { R }$ are given by
$$\mathbf { P } = 5 \mathbf { i } + 4 \mathbf { j } , \quad \mathbf { Q } = 3 \mathbf { i } - 5 \mathbf { j } , \quad \mathbf { R } = - 8 \mathbf { i } + \mathbf { j }$$
\begin{enumerate}[label=(\roman*)]
\item Find the vector $\mathbf { P } + \mathbf { Q } + \mathbf { R }$.
\item Interpret your answer to part (i) in the cases\\
(A) $\mathbf { P } , \mathbf { Q }$ and $\mathbf { R }$ represent three forces acting on a particle,\\
(B) $\mathbf { P } , \mathbf { Q }$ and $\mathbf { R }$ represent three stages of a hiker's walk.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M1 Q2 [3]}}