| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2019 |
| Session | Specimen |
| Marks | 6 |
| 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. It's purely procedural with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple standard steps. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
\includegraphics{figure_6}
The diagram shows two horizontal forces $\mathbf{P}$ and $\mathbf{Q}$ acting at the origin $O$ of rectangular coordinates $Oxy$. 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.
\begin{enumerate}[label=(\alph*)]
\item Write down the components, in the $x$- and $y$-directions, of the resultant of $\mathbf{P}$ and $\mathbf{Q}$. [2]
\item Hence, or otherwise, calculate the magnitude of this resultant and the angle the resultant makes with the positive $x$-axis. [4]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2019 Q6 [6]}}