Vectors — AS & A Level Mathematics (9709) questions by topic
Finding an unknown coordinate from equal vector magnitudes, working out a unit vector along a given line, and finding where two skew lines meet or the angle between their directions are typical of the 16 vector questions from 2023 to 2025, worth 7 to 12 marks.
Find, show and calculate top the command words, with state and determine used for shorter vector-equation results. Vectors here mean magnitude-and-direction arithmetic in three dimensions, distinct from the scalar algebra elsewhere in the syllabus, so each dot-product or magnitude calculation is marked on its own working. Submit your vector solutions for instant marking to catch a mismatched component or a sign slip in a cross-product line before it derails the full answer.
May–June 2025, Paper 31
With respect to the origin O, the points A and B have position vectors 2i + 4k and 5i + j + 6k respectively. The line l₁ passes through the points A and B. Find a vector equation…
Answer this question and get it marked →May–June 2025, Paper 32
With respect to the origin O, the points A, B and C have position vectors given by OA = (1, -4, 2), OB = (-2, 1, 3) and OC = (2, 3, 5) (each written as a column vector). Find a…
Answer this question and get it marked →May–June 2025, Paper 33
With respect to the origin O, the points A, B and C have position vectors given by OA = i + 2j, OB = i + 3j − 2k, and OC = 2i − j + 3k. The line l passes through B and C. Find a…
Answer this question and get it marked →May–June 2025, Paper 35
With respect to the origin O, the points A, B and C have position vectors given by OA = 2i − j − 6k, OB = bi − 2j + 3k and OC = −4i + 5j − 2k. It is given that AB = BC . Find the…
Answer this question and get it marked →May–June 2024, Paper 31
The equations of two straight lines l₁ and l₂ are l₁: r = i − 2j + 3k + λ(2i − j + ak) and l₂: r = −i − j − k + μ(3i − 2j − 2k), where a is a constant. The lines l₁ and l₂ are…
Answer this question and get it marked →May–June 2024, Paper 32
The points A, B and C have position vectors OA = -2i + j + 4k, OB = 5i + 2j and OC = 8i + 5j - 3k, where O is the origin. The line l1 passes through B and C. Find a vector…
Answer this question and get it marked →May–June 2024, Paper 33
The equations of two straight lines are r = i + j + 2ak + λ(3i + 4j + ak) and r = −3i − j + 4k + μ(−i + 2j + 2k), where a is a constant. Given that the acute angle between the…
Answer this question and get it marked →October–November 2024, Paper 31
The position vector of point A relative to the origin O is OA = 8i − 5j + 6k. The line l passes through A and is parallel to the vector 2i + j + 4k. State a vector equation for l.
Answer this question and get it marked →October–November 2024, Paper 32
With respect to the origin O, the points A, B and C have position vectors given by OA = (2, 1, −3), OB = (0, 4, 1) and OC = (−3, −2, 2) (each written as a column vector). The…
Answer this question and get it marked →October–November 2024, Paper 33
The lines l and m have vector equations l: r = 2i + j − 3k + λ(−i + 2k) and m: r = 2i + j − 3k + μ(2i − j + 5k). Lines l and m intersect at the point P. State the coordinates of P.
Answer this question and get it marked →May–June 2023, Paper 31
Relative to the origin O, the points A, B and C have position vectors given by (as column vectors) OA = (2, 1, 3), OB = (4, 3, 2) and OC = (3, −2, −4). The quadrilateral ABCD is a…
Answer this question and get it marked →May–June 2023, Paper 32
The points A and B have position vectors i + 2j − 2k and 2i − j + k respectively. The line l has equation r = i − j + 3k + μ(2i − 3j + 4k). Show that l does not intersect the line…
Answer this question and get it marked →May–June 2023, Paper 33
The lines l and m have equations l: r = a i + 3 j + b k + λ(c i − 2 j + 4 k), m: r = i + 2 j + 3 k + μ(2 i − 3 j + k). Relative to the origin O, the position vector of the point P…
Answer this question and get it marked →October–November 2023, Paper 31
In the diagram, OABCDEFG is a cuboid in which OA = 3 units, OC = 2 units and OD = 2 units. Unit vectors i, j and k are parallel to OA, OD and OC respectively. M is the midpoint of…
Answer this question and get it marked →October–November 2023, Paper 32
The equations of the lines l and m are given by l: r = (3, −2, 1) + λ(1, 1, 2) and m: r = (6, −3, 6) + μ(−2, 4, c), where the position and direction vectors are column vectors and…
Answer this question and get it marked →October–November 2023, Paper 33
The line l has equation r = i − 2j − 3k + λ(−i + j + 2k). The points A and B have position vectors −2i + 2j − k and 3i − j + k respectively. Find a unit vector in the direction of…
Answer this question and get it marked →Other AS & A Level Mathematics topics
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