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Finding a Vector by Following a Path

Part of Vectors (Geometry Proofs) — GCSE Mathematics

This deep dive covers Finding a Vector by Following a Path 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 3 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 11

Practice

14 questions

Recall

12 flashcards

Finding a Vector by Following a Path

In a diagram, you cannot always go directly from one point to another along a labelled arrow. Instead, trace a route through points you do know, adding or subtracting vectors as you go.

Rule: To travel from point P to point Q, add the vectors for each step of the journey. If you travel against an arrow, negate that vector.

Keep building this topic

Read this section alongside the surrounding pages in Vectors (Geometry Proofs). That gives you the full topic sequence instead of a single isolated revision point.

Vector Notation RecapPath FormulaVectors in Geometry: Proving What You Can SeeWorked Example: Midpoint Vector

Practice 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

Quick Recall 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.

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Vector Notation Recap

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Path Formula