| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2016 |
| Session | Specimen |
| Marks | 7 |
| Topic | Vectors Introduction & 2D |
| Type | Resultant of three coplanar forces |
| Difficulty | Easy -1.2 This is a straightforward vector addition problem requiring only basic component addition and then magnitude/angle calculation using Pythagoras and arctangent. The components are given explicitly, making this simpler than average A-level mechanics questions which often require resolving forces first. It's routine bookwork with no problem-solving insight needed. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors3.03a Force: vector nature and diagrams3.03p Resultant forces: using vectors |
**(i)** $x = 7$ **B1**
$y = 24$ (award B1 only if not identified) **B1**
**(ii)** $r^2 = 7^2 + 24^2$ **M1**
Magnitude is $25$ N **A1**
$\tan\theta = \frac{24}{7}$ **M1**
Angle is $73.7°$ **A1**6\\
\includegraphics[max width=\textwidth, alt={}, center]{b18b1bc5-bf26-4161-b5a5-764b00e97bea-4_572_672_456_701}
The diagram shows two horizontal forces $\mathbf { P }$ and $\mathbf { Q }$ acting at the origin $O$ of rectangular coordinates $O x y$. The components of $\mathbf { P }$ in the $x$ - and $y$-directions are 12 N and 17 N respectively. The components of $\mathbf { Q }$ in the $x$ - and $y$-directions are - 5 N and 7 N respectively.\\
(i) Write down the components, in the $x$ - and $y$-directions, of the resultant of $\mathbf { P }$ and $\mathbf { Q }$.\\
(ii) Hence, or otherwise, calculate the magnitude of this resultant and the angle the resultant makes with the positive $x$-axis.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2016 Q6 [7]}}