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9709 past papers

9709 · topic questions

Vectors

Mathematics12 questions

12 past-paper questions on Vectors

  • 9709/33 · May/June 20246 marks

    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…

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  • 9709/32 · October/November 20245 marks

    The diagonals of the trapezium intersect at the point P. Find the position vector of P.

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  • 9709/32 · May/June 20245 marks

    The point D on l₂ is such that AB = BD. Find the position vector of D.

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  • 9709/33 · May/June 20245 marks

    Given instead that the lines intersect, find the value of a and the position vector of the point of intersection.

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  • 9709/31 · October/November 20245 marks

    The line m has vector equation r = 5i−j+2k+μ(ai-j+3k). The acute angle between the directions of l and m is θ, where cosθ = 1/√6.…

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  • 9709/32 · May/June 20244 marks

    The line l₂ has equation r = −2i+j+4k+µ(3i+j – 2k). Find the coordinates of the point of intersection of l₁ and l₂.

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  • 9709/32 · October/November 20244 marks

    Using a scalar product, calculate angle ABC.

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  • 9709/32 · May/June 20254 marks

    Using a scalar product, find the exact value of cos BAC.

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  • 9709/31 · May/June 20244 marks

    The lines l₁ and l₂ also intersect. (b) Find the position vector of the point of intersection.

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  • 9709/33 · May/June 20254 marks

    The point P is the foot of the perpendicular from A to l. Find the position vector of P.

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  • 9709/33 · October/November 20243 marks

    The point A on line l has coordinates (0,1,1). The point B on line m has coordinates (0,2, -8). Find the exact area of triangle…

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  • 9709/32 · May/June 20243 marks

    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…

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Vectors (9709) past-paper questions — marked instantly

These are real Cambridge Mathematics past-paper questions on Vectors. Open one, attempt it, then upload your working — MarkScheme grades it against the official 9709 mark scheme so you see exactly where the marks are won and lost on this topic.

Frequently asked questions

How many Vectors questions are there for 9709?
This page collects 12 recent Cambridge Mathematics (9709) past-paper questions tagged to Vectors. Each links straight to instant marking against the official 9709 scheme.
How are Vectors answers marked?
Type or photograph your working and MarkScheme scores it against the real 9709 mark scheme for this topic — method, accuracy and any band descriptors — so you see exactly where the marks are.
Where can I learn Vectors first?
Start with the free Mathematics lesson on Vectors, then come back and drill past-paper questions under timed conditions.