OxNotes GCSE Revision
  • Home 🏡
  • AIC
  • GCSE/IGCSE
    • GCSE English Literature
    • IGCSE Physics
    • IGCSE Biology
    • IGCSE Chemistry
    • IGCSE Mathematics
    • GCSE Geography
    • GCSE Economics
    • GCSE History
    • MORE GCSE/IGCSE Subjects...
  • 🔎
  • Learn Faster 🔥

You are here: OxNotes Home › GCSE/IGCSE Notes › Maths › Vectors

Simple explanation of Vectors

A vector is a quantity with magnitude (size/length) and direction. If two vectors have the same magnitude and direction, they're equal. Equal vectors are parallel.

Column Vectors

A column vector has an x-part (top) and a y-part (bottom).
  • Positive x = right, negative x = left. 
  • Positive y = up, negative y= down.
You can remember which one is which through picturing the values as an xy graph. The top (x-part) is horizontal (left or right), while the bottom (y-part) is vertical (up or down).

Finding Column Vectors from Coordinates

  • Method One: Plot the coordinates and find column vector by inspection.
  • Method Two: Calculate. Find CD by D - C.
eg. C is at (6, -2), D is at (5, 4).
x: 5 - 6 = -1; y: 4 - -2 = 6 → CD

Comparing Column Vectors

E is at (3, -5). F is at (1, 7)
x: 1 - 3 = -2; y: 7 - -5 = 12
EF is twice as long as CD and parallel to it.

Parallel Vectors

Two vectors are parallel if one is a multiple of the other.

Opposite Vectors

Two vectors are opposite if their x and y values are the same but different signs.

Magnitude of a Vector

The magnitude of a vector is simply the length of the line. Use Pythagoras' Theorem to find the magnitude of a vector.

Angle to Horizontal

Use trigonometry (tan) to find the angle a vector makes to the horizontal (or vertical). 

Adding Vectors

Just add the x-parts and y-parts separately. Similarly for subtracting.

Multiplying by a Number

Just multiply the x-parts and y-parts separately by the number.

Parallel to x- a y-axes

Vectors parallel to the x-axis include
i.e. the y-part is zero.
Vectors parallel to the y-axis include
i.e. the x-part is zero.

Related Notes

‹ Back to IGCSE Mathematics
Pythagoras' Theorem
Powered by Create your own unique website with customizable templates.
  • Home 🏡
  • AIC
  • GCSE/IGCSE
    • GCSE English Literature
    • IGCSE Physics
    • IGCSE Biology
    • IGCSE Chemistry
    • IGCSE Mathematics
    • GCSE Geography
    • GCSE Economics
    • GCSE History
    • MORE GCSE/IGCSE Subjects...
  • 🔎
  • Learn Faster 🔥