OCR FP1 AS 2021 June — Question 1 5 marks

Exam BoardOCR
ModuleFP1 AS (Further Pure 1 AS)
Year2021
SessionJune
Marks5
TopicVectors: Cross Product & Distances
TypeVerify perpendicularity using scalar product
DifficultyModerate -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.
Spec4.04a Line equations: 2D and 3D, cartesian and vector forms4.04g Vector product: a x b perpendicular vector

  1. Find a vector which is perpendicular to both \(\begin{pmatrix} 1 \\ 3 \\ -2 \end{pmatrix}\) and \(\begin{pmatrix} -3 \\ -6 \\ 4 \end{pmatrix}\). [2]
  2. 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]

\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]}}