This study notes covers Practice Questions within Vectors (Geometry Proofs) for GCSE Mathematics. Revise Vectors (Geometry Proofs) in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 12 of 12 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Practice Questions
- OA = a, OB = b. M is the midpoint of AB. Write OM in terms of a and b.
- OABC is a parallelogram where OA = a and OC = c. Find OB in terms of a and c.
- OA = 4a, OB = 4b. P is the midpoint of OA, Q is the midpoint of OB. Prove that PQ is parallel to AB.
- OA = a, OB = b. Point C has position vector a + 2b. Point D has position vector 3a + 6b. Prove that O, C and D are not collinear (or check if they are).
- OA = a, OB = b. Point P divides AB in ratio 1:3. Find the position vector of P.
Practice questions for Vectors (Geometry Proofs)
Vector AB goes from point A to point B. Which of the following describes vector BA?
A student says: 'I have shown that vector AB is parallel to vector CD, so A, B, C, D all lie on the same straight line.' Explain why the student's reasoning is incorrect.
Quick recall flashcards
When are two vectors parallel?
Two vectors p and q are parallel when one is a scalar multiple of the other: p = kq for some non-zero scalar k. They point in the same or exactly opposite direction.
If AB = a, what is BA?
BA = -a. Reversing the direction of travel negates the vector. In diagrams: if you travel against an arrow, write a negative sign in front of that vector.