9709 · topic questions
Vectors
12 past-paper questions on Vectors
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…
Practise the full question →The diagonals of the trapezium intersect at the point P. Find the position vector of P.
Practise the full question →The point D on l₂ is such that AB = BD. Find the position vector of D.
Practise the full question →Given instead that the lines intersect, find the value of a and the position vector of the point of intersection.
Practise the full question →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.…
Practise the full question →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.
Practise the full question →Using a scalar product, calculate angle ABC.
Practise the full question →Using a scalar product, find the exact value of cos BAC.
Practise the full question →The lines l₁ and l₂ also intersect. (b) Find the position vector of the point of intersection.
Practise the full question →The point P is the foot of the perpendicular from A to l. Find the position vector of P.
Practise the full question →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…
Practise the full question →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…
Practise the full question →
Question stems are shortened previews. Open a question to attempt the full version and have it marked.
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.