| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Foot of perpendicular from origin to line |
| Difficulty | Standard +0.3 This is a standard two-part vectors question requiring routine techniques: finding a line equation from two points (straightforward vector subtraction), then using the perpendicularity condition (dot product = 0) to find a parameter value. While it involves multiple steps, both are textbook procedures with no novel insight required, making it slightly easier than average. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04c Scalar product: calculate and use for angles |
4 Relative to an origin $O$, the points $A$ and $B$ have position vectors $3 \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k }$ and $\mathbf { i } + 3 \mathbf { j } + 4 \mathbf { k }$ respectively.\\
(i) Find a vector equation of the line passing through $A$ and $B$.\\
(ii) Find the position vector of the point $P$ on $A B$ such that $O P$ is perpendicular to $A B$.
\hfill \mbox{\textit{OCR C4 2008 Q4 [7]}}