| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Show lines intersect and find intersection point |
| Difficulty | Standard +0.3 This is a standard three-part vector lines question requiring routine application of well-practiced techniques: writing vector equations from given information, solving simultaneous equations to find intersection, and using the scalar product formula for angles. While it involves multiple steps and careful algebra, it follows a predictable template with no novel insight required, making it slightly easier than the average A-level question. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04c Scalar product: calculate and use for angles4.04e Line intersections: parallel, skew, or intersecting |
7 The line $L _ { 1 }$ passes through the point $( 3,6,1 )$ and is parallel to the vector $2 \mathbf { i } + 3 \mathbf { j } - \mathbf { k }$. The line $L _ { 2 }$ passes through the point ( $3 , - 1,4$ ) and is parallel to the vector $\mathbf { i } - 2 \mathbf { j } + \mathbf { k }$.\\
(i) Write down vector equations for the lines $L _ { 1 }$ and $L _ { 2 }$.\\
(ii) Prove that $L _ { 1 }$ and $L _ { 2 }$ intersect, and find the coordinates of their point of intersection.\\
(iii) Calculate the acute angle between the lines.
\hfill \mbox{\textit{OCR C4 Q7 [11]}}