| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Forces as vectors |
| Difficulty | Moderate -0.8 This is a straightforward equilibrium problem requiring students to set the sum of three force vectors equal to zero and solve for three unknowns, followed by a routine magnitude calculation. Both parts involve direct application of standard formulas with minimal problem-solving or conceptual challenge. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.03b Newton's first law: equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\begin{pmatrix}x\\-7\\z\end{pmatrix} + \begin{pmatrix}4\\y\\-5\end{pmatrix} + \begin{pmatrix}5\\4\\-7\end{pmatrix} = \begin{pmatrix}0\\0\\0\end{pmatrix}\) | M1 | |
| \(x = -9\) | A1 | [Allow SC 2/4 if \(9, -3, -12\) obtained] |
| \(y = 3\) | A1 | |
| \(z = 12\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| We need \(\sqrt{5^2 + 4^2 + (-7)^2}\) | M1 | |
| \(= \sqrt{90}\) or \(9.48683\ldots\) so \(9.49\) (3 s.f.) | A1 | Any reasonable accuracy |
# Question 5:
## Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\begin{pmatrix}x\\-7\\z\end{pmatrix} + \begin{pmatrix}4\\y\\-5\end{pmatrix} + \begin{pmatrix}5\\4\\-7\end{pmatrix} = \begin{pmatrix}0\\0\\0\end{pmatrix}$ | M1 | |
| $x = -9$ | A1 | [Allow SC 2/4 if $9, -3, -12$ obtained] |
| $y = 3$ | A1 | |
| $z = 12$ | A1 | |
## Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| We need $\sqrt{5^2 + 4^2 + (-7)^2}$ | M1 | |
| $= \sqrt{90}$ or $9.48683\ldots$ so $9.49$ (3 s.f.) | A1 | Any reasonable accuracy |
---5 A particle is in equilibrium when acted on by the forces $\left( \begin{array} { r } x \\ - 7 \\ z \end{array} \right) , \left( \begin{array} { r } 4 \\ y \\ - 5 \end{array} \right)$ and $\left( \begin{array} { r } 5 \\ 4 \\ - 7 \end{array} \right)$, where the units are newtons.\\
(i) Find the values of $x , y$ and $z$.\\
(ii) Calculate the magnitude of $\left( \begin{array} { r } 5 \\ 4 \\ - 7 \end{array} \right)$.
\hfill \mbox{\textit{OCR MEI M1 Q5 [6]}}