| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Area of triangle from given side vectors or coordinates |
| Difficulty | Standard +0.3 This is a straightforward multi-part vector question requiring standard techniques: dot product for angle (part i), cross product magnitude for area (part ii), and perpendicular distance formula (part iii). All methods are routine C4 content with no novel insight required, making it slightly easier than average. |
| Spec | 1.10c Magnitude and direction: of vectors4.04c Scalar product: calculate and use for angles4.04g Vector product: a x b perpendicular vector |
4. Relative to a fixed origin, $O$, the points $A$ and $B$ have position vectors $\left( \begin{array} { c } 1 \\ 5 \\ - 1 \end{array} \right)$ and $\left( \begin{array} { c } 6 \\ 3 \\ - 6 \end{array} \right)$ respectively.
Find, in exact, simplified form,\\
(i) the cosine of $\angle A O B$,\\
(ii) the area of triangle $O A B$,\\
(iii) the shortest distance from $A$ to the line $O B$.\\
\hfill \mbox{\textit{OCR C4 Q4 [9]}}