Further vectors questions

Practice questions covering further vectors from this specification. Attempt the questions below; real-paper references for this topic are being imported.

Questions to attempt

6 questions on Further vectors, each with its mark scheme and worked method. Reveal the answer when you have had a go.

FP1-5.1 · The vector product a x b of two vectors.
Q1
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
1.
Find the area of the triangle with vertices $A(1,0,2)$ , $B(3,1,-1)$ and $C(2,4,1)$ , giving your answer in surd form.
(5)
(Total for Question 1 is 5 marks)
FP1-5.1 · The vector product a x b of two vectors.
Q2
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
2.
Given $\mathbf{a}=3\mathbf{i}+\mathbf{j}-2\mathbf{k}$ and $\mathbf{b}=\mathbf{i}+4\mathbf{j}+\mathbf{k}$ , find $\mathbf{a}\times\mathbf{b}$ .
(3)
(Total for Question 2 is 3 marks)
FP1-5.2 · The scalar triple product a.b x c.
Q3
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
3.
Find the volume of the tetrahedron with vertices $O(0,0,0)$ , $A(1,0,2)$ , $B(2,3,0)$ and $C(0,1,4)$ .
(4)
(Total for Question 3 is 4 marks)
FP1-5.2 · The scalar triple product a.b x c.
Q4
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
4.
Given $\mathbf{a}=\mathbf{i}+2\mathbf{j}+3\mathbf{k}$ , $\mathbf{b}=\mathbf{j}+4\mathbf{k}$ and $\mathbf{c}=2\mathbf{i}+\mathbf{k}$ , find $\mathbf{a}\cdot\left(\mathbf{b}\times\mathbf{c}\right)$ .
(3)
(Total for Question 4 is 3 marks)
FP1-5.3 · Applications of vectors to three dimensional geometry involving points, lines and planes.
Q5
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
5.
Find the Cartesian equation of the plane through the point $(1,2,-1)$ with normal vector $2\mathbf{i}-\mathbf{j}+3\mathbf{k}$ .
(3)
(Total for Question 5 is 3 marks)
FP1-5.3 · Applications of vectors to three dimensional geometry involving points, lines and planes.
Q6
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
6.
Write the line through $(1,2,3)$ with direction $2\mathbf{i}-\mathbf{j}+4\mathbf{k}$ in the form $\left(\mathbf{r}-\mathbf{a}\right)\times\mathbf{b}=\mathbf{0}$ and in Cartesian form.
(3)
(Total for Question 6 is 3 marks)

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Printable question pack — FP1-5 Further vectors (Further Pure 1)All 30 questions across 3 specification points — 24 more than the 6 above — with the full mark scheme. Guest accessible · browser print.

FP1-5 Further vectors (Further Pure 1) revision notes

Real-paper references

Real-paper references for this module are being imported — the questions above are the site's own, exam-faithful, marked.

Reference rows contain series, paper, question number, marks and classification metadata only. Pearson's question papers open on Pearson's own website.

Questions to attempt

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