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Vectors (Geometry Proofs)

Revise Vectors (Geometry Proofs) in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency exam topic, so students should expect to explain it clearly under timed conditions.

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1

Vectors in Geometry: Proving What You Can See

Introduction2

Knowledge Organiser: Vectors — Geometry Proofs

Summary3

Vector Notation Recap

Key Facts4

Finding a Vector by Following a Path

Deep Dive5

Path Formula

Equations6

Worked Example: Midpoint Vector

Deep Dive7

Proving Two Lines Are Parallel

Deep Dive8

Proving Three Points Are Collinear

Deep Dive9

Points Dividing a Line in a Given Ratio

Deep Dive10

Key Results to Remember

Key Facts11

Exam Tips

Exam Tips12

Practice Questions

Notes

Sample Flashcards

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.
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.

Exam questions for Vectors (Geometry Proofs)

Vector AB goes from point A to point B. Which of the following describes vector BA?

  • A. The same vector as AB
  • B. Twice the length of AB in the same direction
  • C. The same magnitude as AB but in the opposite direction
  • D. Half the length of AB in the opposite direction
1 markfoundation

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.

2 marksstandard

Want more? See all GCSE Mathematics exam questions by paper with full model answers and mark schemes.

14

exam-style questions

12

revision flashcards

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