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Geometry & MeasuresKey Facts

Vector Operations

Part of Vectors (Basics) — GCSE Mathematics

This key facts covers Vector Operations within Vectors (Basics) for GCSE Mathematics. Revise Vectors (Basics) in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 5 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 3 of 6 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 6

Practice

12 questions

Recall

5 flashcards

Vector Operations

Operation Method Example
Addition Add components (3,4) + (1,2) = (4,6)
Subtraction Subtract components (5,7) - (2,3) = (3,4)
Scalar Multiple Multiply each component 3(2,1) = (6,3)
Magnitude |a| = √(x² + y²) |(3,4)| = √(9+16) = 5

Keep building this topic

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

Vector NotationMethod: Finding MagnitudeDirection and DistanceWorked Example: Vector Addition

Practice Questions for Vectors (Basics)

A column vector is written as (3 / −2) (3 on top, −2 on bottom). What does this vector represent?

  • A. 3 units left and 2 units up
  • B. 3 units right and 2 units down
  • C. 3 units up and 2 units right
  • D. 2 units right and 3 units up
1 markfoundation

Explain what it means for two vectors to be parallel. Give an example of a vector that is parallel to a = (2, −3), and one that is parallel but in the opposite direction.

3 marksstandard

Quick Recall Flashcards

Vector Addition
Add components separately. (a,b) + (c,d) = (a+c, b+d). Represents combined movement.
Vector Magnitude
|v| = √(x² + y²). Length of vector using Pythagoras. Always positive!

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Vector Notation

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Method: Finding Magnitude