# Topic Questions: • determine whether two lines are parallel, intersect or are skew, and find the point of intersection of two lines when it exists — 9709 P3 Vectors

> 22 9709 P3 Vectors topic questions (89 marks) on determine whether two lines are parallel… — 21 papers, 2020–2026. Open the exact question in the original…

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CIE IAL · Mathematics · 9709 P3 · Vectors

22 9709 P3 Vectors topic questions are tagged to this syllabus point across 21 papers (2020–2026). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved.

- 22 topic questions
- 21 papers
- 89 tagged marks
- 16.5% of topic questions
- 18.9% of topic marks
- 2020–2026
- Syllabus 2020–2027
- [All 9709 P3 Vectors topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**This Vectors syllabus point appears in 21 9709 P3 papers across 2020–2026, contributing 22 topic questions and 89 marks.** The most recent appearance is 9709/31 May/June 2026. That equals 16.5% of the 133 topic questions and 18.9% of the 470 marks tagged to Vectors. Only parts tagged to this subtopic are counted, so a four-part question can contribute one item and one part's marks. The table lists every matching question, its tagged parts and marks, with a link back to the paper page. Sessions are newest first, so the statement can be traced back through the full paper history.

## Topic questions by session

Newest sessions first. Parts and marks count only the parts tagged to this subtopic; “x of y parts” shows how much of the question is tagged elsewhere. Select the paper cell to open the matching question on the paper page, or use **Go to Practice Hub** to answer that exact question in the Interactive Practice Hub.

| Paper | Question | Type | Parts | Marks | Difficulty | Practice |
| --- | --- | --- | --- | --- | --- | --- |
| [**9709/31** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-may-june-9709-31/#q-9) | **Q9** 3D Line Vector Equations and Skew Lines - CIE Pure Mathematics 2026 Q9 | FRQ | 1 of 2 parts ((b)) | 5 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=5a21f0d9-d2ad-4ffc-9254-eb21daddd8fc&question_id=45a0225f-a221-460b-af9c-26ec5cfb5b04&source_detail=9709%2F31+May%2FJune+2026) |
| [**9709/32** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-may-june-9709-32/#q-9) | **Q9** 3D Lines and Geometry - CIE A Level Mathematics 2026 June Paper 32 Q9 | FRQ | 1 of 3 parts ((b)) | 4 of 12 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d6e975a2-e88a-4b40-82f8-1078f926f377&question_id=cd6f12f0-94d4-4f5c-8fbc-ab0aa0e87ab3&source_detail=9709%2F32+May%2FJune+2026) |
| [**9709/31** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-31/#q-11) | **Q11** Vector Equations of Lines and Intersection - CIE Pure Mathematics 2025 Nov Q11 | FRQ | 1 of 3 parts ((b)) | 4 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7ffa0858-5cbd-490e-9150-de28164f7cda&question_id=1ceb795c-0d70-4a7d-b79c-54d0217dfd0c&source_detail=9709%2F31+October%2FNovember+2025) |
| [**9709/33** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-33/#q-9) | **Q9** 3D Vectors and Lines - CIE Pure Mathematics 2025 Nov Paper 33 Q9 | FRQ | 1 of 3 parts ((c)) | 3 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=17e7e425-f366-4dd8-9a85-08207772196f&question_id=296267af-7e96-4a01-8274-da8a86d8b186&source_detail=9709%2F33+October%2FNovember+2025) |
| [**9709/35** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-35/#q-9) | **Q9** 3D Line Vectors Intersecting and Angle - CIE A Level Mathematics 2025 Winter Paper 35 Q9 | FRQ | 1 of 3 parts ((b)) | 4 of 10 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2b303406-630f-44c2-814e-7e47fa277f61&question_id=f4675f07-0c54-44df-8782-a7911e481fb5&source_detail=9709%2F35+October%2FNovember+2025) |
| [**9709/31** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-31/#q-8) | **Q8** 3D Vector Lines and Intersection - CIE Pure Mathematics 2025 Jun Paper 31 Q8 | FRQ | 1 of 3 parts ((b)) | 4 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d305e649-31d7-4036-b6fa-6295b81b011f&question_id=04ffaed4-7682-4b03-94c8-12727e49556f&source_detail=9709%2F31+May%2FJune+2025) |
| [**9709/32** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-march-9709-32/#q-8) | **Q8** Skew Lines and Angle Calculation - CIE A-Level Math 2025 Mar Paper 32 Q8 | FRQ | 1 of 2 parts ((a)) | 5 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ebe23b18-f2b2-4e16-8e60-c5ac5649cb15&question_id=f4e99aa7-eb01-4f8a-96b5-4674b80b2dea&source_detail=9709%2F32+March+2025) |
| [**9709/31** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-31/#q-9) | **Q9** Vector Lines and Scalar Product Angle - CIE A-Level Maths 2024 Nov Paper 31 Q9 | FRQ | 1 of 3 parts ((b)) | 3 of 10 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=70a34762-5adb-4bbc-a073-ccdcbf562e7c&question_id=9cad4b53-fea2-45bc-a8f7-710f8397f152&source_detail=9709%2F31+October%2FNovember+2024) |
| [**9709/33** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-33/#q-6) | **Q6** Vector Line Intersections and Triangle Area - CIE A-Level Pure Mathematics 2024 Nov Q6 | FRQ | 1 of 3 parts ((a)) | 1 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=eea0ef07-a2e6-40ec-b1f1-0940ce02a199&question_id=a016d212-de0c-4871-85e9-b90d82716ba5&source_detail=9709%2F33+October%2FNovember+2024) |
| [**9709/31** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-31/#q-9) | **Q9** Perpendicular Lines and Reflection in 3D Vectors - CIE A-Level Maths 2024 Jun Paper 31 Q9 | FRQ | 1 of 4 parts ((b)) | 4 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d001bb3e-de7a-4991-8014-a2761a618aba&question_id=7aeb26d5-e3fa-43ef-9f2f-43ad452e0fb7&source_detail=9709%2F31+May%2FJune+2024) |
| [**9709/32** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-32/#q-8) | **Q8** Vector Equations of Lines and Point of Intersection - CIE A Level Mathematics 2024 Jun P32 Q8 | FRQ | 1 of 3 parts ((b)) | 4 of 12 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b47257e0-776e-40f2-b0b7-69834ea85d57&question_id=2d916b14-354d-4235-8098-d24de8b1c101&source_detail=9709%2F32+May%2FJune+2024) |
| [**9709/33** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-33/#q-10) | **Q10** Angle Between 3D Lines and Intersection - CIE A-Level Pure Mathematics | FRQ | 1 of 2 parts ((b)) | 5 of 11 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7e0feb6b-4f09-4f55-8eeb-a9c09d82ec52&question_id=1ac33a52-995e-4368-aacb-8fb00fd827fe&source_detail=9709%2F33+May%2FJune+2024) |
| [**9709/33** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-october-november-9709-33/#q-11) | **Q11** Vector Lines Intersection and Skew - CIE A-Level Maths 2023 Q11 | FRQ | 1 of 3 parts ((c)) | 5 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=719f9f72-ffe6-4873-b35f-05b84c1bcd86&question_id=85f61f2f-ac0b-4539-a50a-449446bcc5e5&source_detail=9709%2F33+October%2FNovember+2023) |
| [**9709/32** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-may-june-9709-32/#q-11) | **Q11** Skew Lines and Perpendicular Foot in 3D Vectors - CIE Pure Mathematics 2023 Q11 | FRQ | 1 of 2 parts ((a)) | 5 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=07774ae7-6d21-4646-8307-908dbae6fe03&question_id=4faa4ab2-23fe-46d7-a0d1-2b98f0692faa&source_detail=9709%2F32+May%2FJune+2023) |
| [**9709/32** March 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-march-9709-32/#q-10) | **Q10** Angle and Intersection of 3D Lines - CIE Pure Mathematics 2023 Mar Paper 32 Q10 | FRQ | 1 of 3 parts ((c)) | 4 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=fb85986e-2f5e-482c-8e08-173425b67cc3&question_id=1c138a20-8091-4d23-a5fc-6235765f3461&source_detail=9709%2F32+March+2023) |
| [**9709/33** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-october-november-9709-33/#q-9) | **Q9** Vector Geometry and Intersection of Lines - CIE Pure Mathematics 3 | FRQ | 1 of 3 parts ((c)) | 4 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=955ef535-8636-46dc-9b2a-f083375bbec1&question_id=3540a110-81b2-4907-9d4b-6f81d42452ae&source_detail=9709%2F33+October%2FNovember+2022) |
| [**9709/32** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-32/#q-9) | **Q9** 3D Lines Intersection and Perpendicularity - CIE Mathematics 2022 Jun Q9 | FRQ | 2 of 3 parts ((a), (c)) | 6 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6ad396ce-ab9f-4c82-bba2-087b907a1ea1&question_id=62f77f1b-3eb5-4ecd-9c3f-3b8e5f1dea9b&source_detail=9709%2F32+May%2FJune+2022) |
| [**9709/32** March 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-march-9709-32/#q-10) | **Q10** 3D Lines and Vectors - CIE A Level Mathematics 2022 Mar Paper 32 Q10 | FRQ | 1 of 3 parts ((c)) | 4 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=494ba528-51f5-41a2-babf-2cc4c40fecf4&question_id=bfc43a44-d40b-44fa-b667-75d0480355c1&source_detail=9709%2F32+March+2022) |
| [**9709/32** March 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-march-9709-32/#q-7) | **Q7** Skew Lines and Angle Between Vectors - CIE A-Level Mathematics 2021 March Paper 32 Q7 | FRQ | 1 of 2 parts ((a)) | 5 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ab7133da-61cb-4438-b5f6-ad6909bb250e&question_id=83543bf8-754a-477e-80e1-900b125bd5b4&source_detail=9709%2F32+March+2021) |
| [**9709/31** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-october-november-9709-31/#q-11) | **Q11** 3D Line Intersections and Vector Angles - CIE 9709 W20 P31 Q11 | FRQ | 1 of 2 parts ((a)) | 5 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=6981fda4-c850-4a06-b8ec-fc6be77cba56&source_detail=9709%2F31+October%2FNovember+2020) |
| [**9709/33** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-october-november-9709-33/#q-11) | **Q11** Line Intersections and Angles in 3D Vectors - CIE Pure Mathematics 2020 Nov Paper 33 Q11 | FRQ | 1 of 2 parts ((a)) | 5 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=086627cb-e617-484f-abc7-431aab41e928&question_id=45526844-c8a9-4c2c-a2aa-6254f1da5423&source_detail=9709%2F33+October%2FNovember+2020) |

## Related topic questions in Vectors

- [• calculate the magnitude of a vector, and use unit vectors, displacement vectors and position vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/calculate-the-magnitude-of-a-vector-and-use-unit-vectors-displacement-vectors-and/) — 25 question items · 19 papers — 90 marks · 2020–2026
- [• carry out addition and subtraction of vectors and multiplication of a vector by a scalar, and interpret these operations in geometrical terms](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/carry-out-addition-and-subtraction-of-vectors-and-multiplication-of-a-vector-by-a/) — 12 question items · 12 papers — 35 marks · 2020–2025
- [• understand the significance of all the symbols used when the equation of a straight line is expressed in the form $\mathbf{r}=\mathbf{a}+t\mathbf{b}$, and find the equation of a line, given sufficient information](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/understand-the-significance-of-all-the-symbols-used-when-the-equation-of-a-straight/) — 27 question items · 26 papers — 81 marks · 2020–2026
- [• use formulae to calculate the scalar product of two vectors, and use scalar products in problems involving lines and points](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/use-formulae-to-calculate-the-scalar-product-of-two-vectors-and-use-scalar-products/) — 53 question items · 37 papers — 207 marks · 2020–2026
- [• use standard notations for vectors, i.e. $\begin{pmatrix}x\\y\end{pmatrix}$, $x\mathbf{i}+y\mathbf{j}$, $\begin{pmatrix}x\\y\\z\end{pmatrix}$, $x\mathbf{i}+y\mathbf{j}+z\mathbf{k}$, $\overrightarrow{AB}$, $\mathbf{a}$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/use-standard-notations-for-vectors-i-e-begin-pmatrix-x-y-end-pmatrix-x-mathbf-i-y/) — 3 question items · 3 papers — 11 marks · 2020–2022

## Topic question rules and edge cases

**How many topic questions cover this syllabus point?**

21 question stems cover this subtopic across 21 papers, but only 22 tagged parts and 89 marks belong to it. Other parts of the same questions are assessed under different statements and are excluded from this page.

**Which papers include this subtopic?**

The table lists every matching session from 2020–2026. Each row links to the question anchor on the paper page, where the full paper context and practice entry point are available.

**Why can one question appear under several subtopics?**

The parts of one question can assess different syllabus statements. Each part is counted under its own subtopics, so the same question stem can appear on several subtopic pages while each page lists only the parts and marks tagged to that statement.

**Can I practise these questions with AI marking?**

Yes. Open a paper from the table and use the Interactive Practice Hub entry point. The page itself is static HTML so search engines and retrieval agents can read the full question list without executing JavaScript.

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Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/determine-whether-two-lines-are-parallel-intersect-or-are-skew-and-find-the-point-of/