AQA Further Paper 2 2021 June — Question 3 1 marks

Exam BoardAQA
ModuleFurther Paper 2 (Further Paper 2)
Year2021
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors 3D & Lines
TypeParallel and perpendicular lines
DifficultyEasy -1.2 This is a straightforward multiple-choice question requiring only the recall that perpendicular lines have direction vectors with zero dot product. Students compute the dot product of (-1, -2, 5) with each option's direction vector until finding one that equals zero—a routine mechanical check with no problem-solving or insight required.
Spec4.04a Line equations: 2D and 3D, cartesian and vector forms4.04c Scalar product: calculate and use for angles

3 The line \(L\) has equation \(\mathbf { r } = \left[ \begin{array} { l } 3 \\ 2 \\ 0 \end{array} \right] + \lambda \left[ \begin{array} { c } - 1 \\ - 2 \\ 5 \end{array} \right]\) Which of the following lines is perpendicular to the line \(L\) ?
Tick \(( \checkmark )\) one box. $$\begin{aligned} & \mathbf { r } = \left[ \begin{array} { c } 2 \\ - 3 \\ 4 \end{array} \right] + \mu \left[ \begin{array} { c } 1 \\ 2 \\ - 5 \end{array} \right] \\ & \mathbf { r } = \left[ \begin{array} { l } 1 \\ 0 \\ 1 \end{array} \right] + \mu \left[ \begin{array} { c } 2 \\ - 3 \\ 1 \end{array} \right] \\ & \mathbf { r } = \left[ \begin{array} { l } 1 \\ 2 \\ 1 \end{array} \right] + \mu \left[ \begin{array} { l } 1 \\ 1 \\ 2 \end{array} \right] \\ & \mathbf { r } = \left[ \begin{array} { l } 0 \\ 3 \\ 2 \end{array} \right] + \mu \left[ \begin{array} { l } 4 \\ 3 \\ 2 \end{array} \right] \end{aligned}$$ □



Question 3:
AnswerMarks Guidance
\(\mathbf{r} = \begin{bmatrix} 0 \\ 3 \\ 2 \end{bmatrix} + \mu \begin{bmatrix} 4 \\ 3 \\ 2 \end{bmatrix}\)B1 Ticks correct answer
## Question 3:

$\mathbf{r} = \begin{bmatrix} 0 \\ 3 \\ 2 \end{bmatrix} + \mu \begin{bmatrix} 4 \\ 3 \\ 2 \end{bmatrix}$ | B1 | Ticks correct answer
3 The line $L$ has equation $\mathbf { r } = \left[ \begin{array} { l } 3 \\ 2 \\ 0 \end{array} \right] + \lambda \left[ \begin{array} { c } - 1 \\ - 2 \\ 5 \end{array} \right]$

Which of the following lines is perpendicular to the line $L$ ?\\
Tick $( \checkmark )$ one box.

$$\begin{aligned}
& \mathbf { r } = \left[ \begin{array} { c } 
2 \\
- 3 \\
4
\end{array} \right] + \mu \left[ \begin{array} { c } 
1 \\
2 \\
- 5
\end{array} \right] \\
& \mathbf { r } = \left[ \begin{array} { l } 
1 \\
0 \\
1
\end{array} \right] + \mu \left[ \begin{array} { c } 
2 \\
- 3 \\
1
\end{array} \right] \\
& \mathbf { r } = \left[ \begin{array} { l } 
1 \\
2 \\
1
\end{array} \right] + \mu \left[ \begin{array} { l } 
1 \\
1 \\
2
\end{array} \right] \\
& \mathbf { r } = \left[ \begin{array} { l } 
0 \\
3 \\
2
\end{array} \right] + \mu \left[ \begin{array} { l } 
4 \\
3 \\
2
\end{array} \right]
\end{aligned}$$

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\hfill \mbox{\textit{AQA Further Paper 2 2021 Q3 [1]}}