| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Vectors: Cross Product & Distances |
| Type | Verify perpendicularity using scalar product |
| Difficulty | Moderate -0.8 This is a straightforward FP1 question testing basic vector operations: (a) requires computing a cross product using the standard determinant method (2 marks), and (b) involves converting a symmetric form line equation to vector form by reading off a point and direction vector (3 marks). Both parts are routine recall and application of standard techniques with no problem-solving or insight required, making this easier than average even for Further Maths. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04g Vector product: a x b perpendicular vector |
\begin{enumerate}[label=(\alph*)]
\item Find a vector which is perpendicular to both $\begin{pmatrix} 1 \\ 3 \\ -2 \end{pmatrix}$ and $\begin{pmatrix} -3 \\ -6 \\ 4 \end{pmatrix}$. [2]
\item The cartesian equation of a line is $\frac{x}{2} = y - 3 = \frac{z + 4}{4}$.
Express the equation of this line in vector form. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 AS 2021 Q1 [5]}}