| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Angle between two vectors/lines (direct) |
| Difficulty | Moderate -0.5 This is a straightforward application of the scalar product formula for finding angles between vectors. It requires computing the dot product, finding magnitudes using Pythagoras, then applying cos θ = a·b/(|a||b|). While it involves multiple steps and careful arithmetic, it's a standard textbook exercise with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.10b Vectors in 3D: i,j,k notation4.04c Scalar product: calculate and use for angles |
1 Find the angle between the vectors $\mathbf { i } - 2 \mathbf { j } + 3 \mathbf { k }$ and $2 \mathbf { i } + \mathbf { j } + \mathbf { k }$.
\hfill \mbox{\textit{OCR C4 2008 Q1 [4]}}