OCR FP3 — Question 2 7 marks

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors: Cross Product & Distances
TypeAcute angle between line and plane
DifficultyStandard +0.8 This is a Further Pure 3 question requiring finding the angle between a line and plane using vector methods. Students must extract the direction vector, find the plane's normal via cross product, then apply the formula sin θ = |d·n|/(|d||n|). While methodical, it involves multiple computational steps (cross product, dot product, magnitudes) with scope for arithmetic errors, placing it moderately above average difficulty.
Spec4.04d Angles: between planes and between line and plane

Find the acute angle between the line with equation \(\mathbf{r} = 2\mathbf{i} + 3\mathbf{k} + t(\mathbf{i} + 4\mathbf{j} - \mathbf{k})\) and the plane with equation \(\mathbf{r} = 2\mathbf{i} + 3\mathbf{k} + \lambda(\mathbf{i} + 3\mathbf{j} + 2\mathbf{k}) + \mu(\mathbf{i} + 2\mathbf{j} - \mathbf{k})\). [7]

Find the acute angle between the line with equation $\mathbf{r} = 2\mathbf{i} + 3\mathbf{k} + t(\mathbf{i} + 4\mathbf{j} - \mathbf{k})$ and the plane with equation $\mathbf{r} = 2\mathbf{i} + 3\mathbf{k} + \lambda(\mathbf{i} + 3\mathbf{j} + 2\mathbf{k}) + \mu(\mathbf{i} + 2\mathbf{j} - \mathbf{k})$. [7]

\hfill \mbox{\textit{OCR FP3  Q2 [7]}}