| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | June |
| 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 components, followed by standard interpretation of the zero vector in two physical contexts. The calculation is routine (adding i and j components separately), and the interpretations (equilibrium for forces, returning to start for displacement) are textbook applications requiring simple recall rather than problem-solving. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\mathbf{P} + \mathbf{Q} + \mathbf{R} = 0\mathbf{i} + 0\mathbf{j}\) | B1 | Accept answer zero (condone it not being in vector form) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| *(A)* The particle is in equilibrium | B1 | If "equilibrium" is seen give B1. Allow "acceleration is zero", "the particle has constant velocity". Do not allow "The forces are balanced", "The particle is stationary" as complete answers |
| *(B)* The hiker returns to her starting point | B1 | Do not allow "The hiker's displacement is zero" |
# Question 3:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\mathbf{P} + \mathbf{Q} + \mathbf{R} = 0\mathbf{i} + 0\mathbf{j}$ | B1 | Accept answer zero (condone it not being in vector form) |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| *(A)* The particle is in equilibrium | B1 | If "equilibrium" is seen give B1. Allow "acceleration is zero", "the particle has constant velocity". Do not allow "The forces are balanced", "The particle is stationary" as complete answers |
| *(B)* The hiker returns to her starting point | B1 | Do not allow "The hiker's displacement is zero" |
---3 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 2012 Q3 [3]}}