| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2009 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Lines & Planes |
| Type | Angle between two planes |
| Difficulty | Standard +0.3 This is a straightforward application of standard vector techniques: reading normal vectors from plane equations, using the dot product formula for angles between planes, and writing a line equation using a known point and direction vector. All steps are routine with no problem-solving insight required, making it slightly easier than average. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04b Plane equations: cartesian and vector forms4.04c Scalar product: calculate and use for angles4.04d Angles: between planes and between line and plane4.04f Line-plane intersection: find point |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (i) Accurate algebraic simplification to give \(y^2-160y+400=0\) | B1 | |
| (ii) Use of quadratic formula (or other method) to find other root: \(d=157.5\) cm. This is greater than the height of the tank so not possible | M1, A1, E1 |
## Question 5:
| Answer/Working | Marks | Guidance |
|---|---|---|
| (i) Accurate algebraic simplification to give $y^2-160y+400=0$ | B1 | |
| (ii) Use of quadratic formula (or other method) to find other root: $d=157.5$ cm. This is greater than the height of the tank so not possible | M1, A1, E1 | |5 (i) Write down normal vectors to the planes $2 x - y + z = 2$ and $x - z = 1$.\\
Hence find the acute angle between the planes.\\
(ii) Write down a vector equation of the line through $( 2,0,1 )$ perpendicular to the plane $2 x - y + z = 2$. Find the point of intersection of this line with the plane.
\hfill \mbox{\textit{OCR MEI C4 2009 Q5 [8]}}